Dissertations / Theses on the topic 'Number Theory and Field Theory'
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Rozario, Rebecca. "The Distribution of the Irreducibles in an Algebraic Number Field." Fogler Library, University of Maine, 2003. http://www.library.umaine.edu/theses/pdf/RozarioR2003.pdf.
Full textRakotoniaina, Tahina. "Explicit class field theory for rational function fields." Thesis, Link to the online version, 2008. http://hdl.handle.net/10019/1993.
Full textBriggs, Matthew Edward. "An Introduction to the General Number Field Sieve." Thesis, Virginia Tech, 1998. http://hdl.handle.net/10919/36618.
Full textMaster of Science
Hughes, Garry. "Distribution of additive functions in algebraic number fields." Title page, contents and summary only, 1987. http://web4.library.adelaide.edu.au/theses/09SM/09smh893.pdf.
Full textMcLeman, Cameron William. "A Golod-Shafarevich Equality and p-Tower Groups." Diss., The University of Arizona, 2008. http://hdl.handle.net/10150/194026.
Full textSolomon, Y. J. "A critique of psychological theories of number development and a reorientation of the field." Thesis, Lancaster University, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.374154.
Full textSwanson, Colleen M. "Algebraic number fields and codes /." Connect to online version, 2006. http://ada.mtholyoke.edu/setr/websrc/pdfs/www/2006/172.pdf.
Full textBamunoba, Alex Samuel. "Cyclotomic polynomials (in the parallel worlds of number theory)." Thesis, Stellenbosch : Stellenbosch University, 2011. http://hdl.handle.net/10019.1/17865.
Full textENGLISH ABSTRACT: It is well known that the ring of integers Z and the ring of polynomials A = Fr[T] over a finite field Fr have many properties in common. It is due to these properties that almost all the famous (multiplicative) number theoretic results over Z have analogues over A. In this thesis, we are devoted to utilising this analogy together with the theory of Carlitz modules. We do this to survey and compare the analogues of cyclotomic polynomials, the size of their coefficients and cyclotomic extensions over the rational function field k = Fr(T).
AFRIKAANSE OPSOMMING: Dit is bekend dat Z, die ring van heelgetalle en A = Fr[T], die ring van polinome oor ’n eindige liggaam baie eienskappe in gemeen het. Dit is as gevolg van hierdie eienskappe dat feitlik al die bekende multiplikative resultate wat vir Z geld, analoë in A het. In hierdie tesis, fokus ons op die gebruik van hierdie analogie saam met die teorie van die Carlitz module. Ons doen dit om ’n oorsig oor die analoë van die siklotomiese polinome, hul koëffisiënte, en siklotomiese uitbreidings oor die rasionele funksie veld k = Fr(T).
Cipra, James Arthur. "Waring’s number in finite fields." Diss., Kansas State University, 2010. http://hdl.handle.net/2097/4152.
Full textDepartment of Mathematics
Todd E. Cochrane
This thesis establishes bounds (primarily upper bounds) on Waring's number in finite fields. Let $p$ be a prime, $q=p^n$, $\mathbb F_q$ be the finite field in $q$ elements, $k$ be a positive integer with $k|(q-1)$ and $t= (q-1)/k$. Let $A_k$ denote the set of $k$-th powers in $\mathbb F_q$ and $A_k' = A_k \cap \mathbb F_p$. Waring's number $\gamma(k,q)$ is the smallest positive integer $s$ such that every element of $\mathbb F_q$ can be expressed as a sum of $s$ $k$-th powers. For prime fields $\mathbb F_p$ we prove that for any positive integer $r$ there is a constant $C(r)$ such that $\gamma(k,p) \le C(r) k^{1/r}$ provided that $\phi(t) \ge r$. We also obtain the lower bound $\gamma(k,p) \ge \frac {(t-1)}ek^{1/(t-1)}-t+1$ for $t$ prime. For general finite fields we establish the following upper bounds whenever $\gamma(k,q)$ exists: $$ \gamma(k,q)\le 7.3n\left\lceil\frac{(2k)^{1/n}}{|A_k^\prime|-1}\right\rceil\log(k), $$ $$ \gamma(k,q)\le8n \left\lceil{\frac{(k+1)^{1/n}-1}{|A^\prime_k|-1}}\right\rceil, $$ and $$ \gamma(k,q)\ll n(k+1)^{\frac{\log(4)}{n\log|\kp|}}\log\log(k). $$ We also establish the following versions of the Heilbronn conjectures for general finite fields. For any $\ve>0$ there is a constant, $c(\ve)$, such that if $|A^\prime_k|\ge4^{\frac{2}{\ve n}}$, then $\gamma(k,q)\le c(\varepsilon) k^{\varepsilon}$. Next, if $n\ge3$ and $\gamma(k,q)$ exists, then $\gamma(k,q)\le 10\sqrt{k+1}$. For $n=2$, we have $\gamma(k,p^2)\le16\sqrt{k+1}$.
Blackhurst, Jonathan H. "Proven Cases of a Generalization of Serre's Conjecture." Diss., CLICK HERE for online access, 2006. http://contentdm.lib.byu.edu/ETD/image/etd1386.pdf.
Full textKawaguchi, Yuki. "Near Miss abc-Triples in General Number Fields." Kyoto University, 2019. http://hdl.handle.net/2433/242576.
Full textLe, hung Bao Viet. "Modularity of some elliptic curves over totally real fields." Thesis, Harvard University, 2014. http://dissertations.umi.com/gsas.harvard:11464.
Full textMathematics
Simons, Lloyd D. "The structure of the Hilbert symbol for unramified extensions of 2-adic number fields /." Thesis, McGill University, 1986. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=74002.
Full textMcCoy, Daisy Cox. "Irreducible elements in algebraic number fields." Diss., Virginia Tech, 1990. http://hdl.handle.net/10919/39950.
Full textSordo, Vieira Luis A. "ON P-ADIC FIELDS AND P-GROUPS." UKnowledge, 2017. http://uknowledge.uky.edu/math_etds/43.
Full textRada, Ion Kolster Manfred. "The Lichtenbaum conjecture at the prime 2 /." *McMaster only, 2002.
Find full textHymo, John A. "Problems involving relative integral bases for quartic number fields." Diss., Virginia Tech, 1990. http://hdl.handle.net/10919/39404.
Full textPh. D.
Milovic, Djordjo. "On the 16-rank of class groups of quadratic number fields." Thesis, Université Paris-Saclay (ComUE), 2016. http://www.theses.fr/2016SACLS157/document.
Full textWe prove two new density results about 16-ranks of class groups of quadratic number fields. The first of the two is that the class group of Q(sqrt{-p}) has an element of order 16 for one-fourth of prime numbers p that are of the form a^2+c^4 with c even. The second is that the class group of Q(sqrt{-2p}) has an element of order 16 for one-eighth of prime numbers p=-1 (mod 4). These density results are interesting for several reasons. First, they are the first non-trivial density results about the 16-rank of class groups in a family of quadratic number fields. Second, they prove an instance of the Cohen-Lenstra conjectures. Third, both of their proofs involve new applications of powerful sieving techniques developed by Friedlander and Iwaniec. Fourth, we give an explicit description of the 8-Hilbert class field of Q(sqrt{-p}) whenever p is a prime number of the form a^2+c^4 with c even; the lack of such an explicit description for the 8-Hilbert class field of Q(sqrt{d}) is the main obstacle to improving the estimates for the density of positive discriminants d for which the negative Pell equation x^2-dy^2=-1 is solvable. In case of the second result, we give an explicit description of an element of order 4 in the class group of Q(sqrt{-2p}) and we compute its Artin symbol in the 4-Hilbert class field of Q(sqrt{-2p}), thereby generalizing a result of Leonard and Williams. Finally, we prove a power-saving error term for a prime-counting function related to the 16-rank of the class group of Q(sqrt{-2p}), thereby giving strong evidence against a conjecture of Cohn and Lagarias that the 16-rank is governed by a Chebotarev-type criterion
Bauer-Price, Pia. "The Selberg Trace Formula for PSL(2, OK) for imaginary quadratic number fields K of arbitrary class number." Bonn : [s.n.], 1991. http://catalog.hathitrust.org/api/volumes/oclc/26531368.html.
Full textBanaszak, Grzegorz. "Algebraic K-theory of number fields and rings of integers and the Stickelberger ideal /." The Ohio State University, 1990. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487676261012829.
Full textSimmering-Best, Vanessa Renée. "Developing a magic number: the dynamic field theory reveals why visual working memory capacity estimates differ across tasks and development." Diss., University of Iowa, 2008. https://ir.uiowa.edu/etd/213.
Full textHinkel, Dustin. "Constructing Simultaneous Diophantine Approximations Of Certain Cubic Numbers." Diss., The University of Arizona, 2014. http://hdl.handle.net/10150/338879.
Full textHarper, John-Paul. "The class number one problem in function fields." Thesis, Stellenbosch : Stellenbosch University, 2003. http://hdl.handle.net/10019.1/53619.
Full textENGLISH ABSTRACT: In this dissertation I investigate the class number one problem in function fields. More precisely I give a survey of the current state of research into extensions of a rational function field over a finite field with principal ring of integers. I focus particularly on the quadratic case and throughout draw analogies and motivations from the classical number field situation. It was the "Prince of Mathematicians" C.F. Gauss who first undertook an in depth study of quadratic extensions of the rational numbers and the corresponding rings of integers. More recently however work has been done in the situation of function fields in which the arithmetic is very similar. I begin with an introduction into the arithmetic in function fields over a finite field and prove the analogies of many of the classical results. I then proceed to demonstrate how the algebra and arithmetic in function fields can be interpreted geometrically in terms of curves and introduce the associated geometric language. After presenting some conjectures, I proceed to give a survey of known results in the situation of quadratic function fields. I present also a few results of my own in this section. Lastly I state some recent results regarding arbitrary extensions of a rational function field with principal ring of integers and give some heuristic results regarding class groups in function fields.
AFRIKAANSE OPSOMMING: In hierdie tesis ondersoek ek die klasgetal een probleem in funksieliggame. Meer spesifiek ondersoek ek die huidige staat van navorsing aangaande uitbreidings van 'n rasionale funksieliggaam oor 'n eindige liggaam sodat die ring van heelgetalle 'n hoofidealgebied is. Ek kyk in besonder na die kwadratiese geval, en deurgaans verwys ek na die analoog in die klassieke getalleliggaam situasie. Dit was die beroemde wiskundige C.F. Gauss wat eerste kwadratiese uitbreidings van die rasionale getalle en die ooreenstemende ring van heelgetalle in diepte ondersoek het. Onlangs het wiskundiges hierdie probleme ook ondersoek in die situasie van funksieliggame oor 'n eindige liggaam waar die algebraïese struktuur baie soortgelyk is. Ek begin met 'n inleiding tot die rekenkunde in funksieliggame oor 'n eindige liggaam en bewys die analogie van baie van die klassieke resultate. Dan verduidelik ek hoe die algebra in funksieliggame geometries beskou kan word in terme van kurwes en gee 'n kort inleiding tot die geometriese taal. Nadat ek 'n paar vermoedes bespreek, gee ek 'n oorsig van wat alreeds vir quadratiese funksieliggame bewys is. In hierdie afdeling word 'n paar resultate van my eie ook bewys. Dan vermeld ek 'n paar resultate aangaande algemene uitbreidings van 'n rasionale funksieliggaam oor 'n eindige liggaam waar die van ring heelgetalle 'n hoofidealgebied is. Laastens verwys ek na 'n paar heurisitiese resultate aangaande klasgroepe in funksieliggame.
Occhipinti, Thomas. "Mordell-Weil Groups of Large Rank in Towers." Diss., The University of Arizona, 2010. http://hdl.handle.net/10150/194213.
Full textByard, Kevin. "Qualified difference sets : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Mathematics at Massey University, Albany, New Zealand." Massey University, 2009. http://hdl.handle.net/10179/1204.
Full textNyqvist, Robert. "Algebraic Dynamical Systems, Analytical Results and Numerical Simulations." Doctoral thesis, Växjö : Växjö University Press, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:vxu:diva-1142.
Full textFreyhult, Lisa. "Aspects of Yang-Mills Theory : Solitons, Dualities and Spin Chains." Doctoral thesis, Uppsala : Acta Universitatis Upsaliensis : Univ.-bibl. [distributör], 2004. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-4498.
Full textLavallee, Melisa Jean. "Dihedral quintic fields with a power basis." Thesis, University of British Columbia, 2008. http://hdl.handle.net/2429/2788.
Full textAngelakis, Athanasios. "Universal Adelic Groups for Imaginary Quadratic Number Fields and Elliptic Curves." Thesis, Bordeaux, 2015. http://www.theses.fr/2015BORD0180/document.
Full textThe present thesis focuses on two questions that are not obviously related. Namely,(1) What does the absolute abelian Galois group AK of an imaginary quadratic number field K look like, as a topological group?(2) What does the adelic point group of an elliptic curve over Q look like, as a topological group?For the first question, the focus on abelian Galois groups provides us with class field theory as a tool to analyze AK . The older work in this area, which goes back to Kubota and Onabe, provides a description of the Pontryagin dual of AK in terms of infinite families, at each prime p, of so called Ulm invariants and is very indirect. Our direct class field theoretic approach shows that AK contains a subgroup UK of finite index isomorphic to the unit group Oˆ∗ of the profinite completion Oˆ of the ring of integers of K, and provides a completely explicit description of the topological group UK that is almost independent of the imaginary quadratic field K. More precisely, for all imaginary quadratic number fields different from Q(i) and Q(√−2), we have UK ∼= U = Zˆ2 × Y Z/nZ. (n=1)The exceptional nature of Q(√−2) was missed by Kubota and Onabe, and their theorems need to be corrected in this respect.Passing from the ‘universal’ subgroup UK to AK amounts to a group extension problem for adelic groups that may be ‘solved’ by passing to a suitable quotient extension involving the maximal Zˆ-free quotientUK/TK of UK . By ‘solved’ we mean that for each K that is sufficiently small to allow explicit class group computations for K, we obtain a practical algorithm to compute the splitting behavior of the extension. In case the quotient extension is totally non-split, the conclusion is that AK is isomorphic as a topological group to the universal group U . Conversely, any splitting of the p-part of the quotient extension at an odd prime p leads to groups AK that are not isomorphic to U . For the prime 2, the situation is special, but our control of it is much greater as a result of the wealth of theorems on 2-parts of quadratic class groups.Based on numerical experimentation, we have gained a basic under- standing of the distribution of isomorphism types of AK for varying K, and this leads to challenging conjectures such as “100% of all imagi- nary quadratic fields of prime class number have AK isomorphic to the universal group U ”.In the case of our second question, which occurs implicitly in [?, Section 9, Question 1] with a view towards recovering a number field K from the adelic point group E(AK ) of a suitable elliptic curve over K, we can directly apply the standard tools for elliptic curves over number fields in a method that follows the lines of the determination of the structure of Oˆ∗ we encountered for our first question.It turns out that, for the case K = Q that is treated in Chapter 4, the adelic point group of ‘almost all’ elliptic curves over Q is isomorphic to a universal groupE = R/Z × Zˆ × Y Z/nZ (n=1)that is somewhat similar in nature to U . The reason for the universality of adelic point groups of elliptic curves lies in the tendency of elliptic curves to have Galois representations on their group of Q-valued torsion points that are very close to being maximal. For K = Q, maximality of the Galois representation of an elliptic curve E means that E is a so-called Serre-curve, and it has been proved recently by Nathan Jones [?] that ‘almost all’ elliptic curves over Q are of this nature. In fact, universality of E(AK ) requires much less than maximality of the Galois representation, and the result is that it actually requires some effort to construct families of elliptic curves with non-universal adelic point groups. We provide an example at the end of Chapter 4
Rezola, Nolberto. "Unique Prime Factorization of Ideals in the Ring of Algebraic Integers of an Imaginary Quadratic Number Field." CSUSB ScholarWorks, 2015. https://scholarworks.lib.csusb.edu/etd/205.
Full textHori, Kumiko, and Shigeo Yoshida. "Nonlocal memory effects of the electromotive force by fluid motion with helicity and two-dimensional periodicity." Taylor & Francis, 2008. http://hdl.handle.net/2237/13015.
Full textIdrees, Zunera. "Elliptic Curves Cryptography." Thesis, Linnéuniversitetet, Institutionen för datavetenskap, fysik och matematik, DFM, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-17544.
Full textSmith, Benjamin Andrew. "Explicit endomorphisms and correspondences." University of Sydney, 2006. http://hdl.handle.net/2123/1066.
Full textIn this work, we investigate methods for computing explicitly with homomorphisms (and particularly endomorphisms) of Jacobian varieties of algebraic curves. Our principal tool is the theory of correspondences, in which homomorphisms of Jacobians are represented by divisors on products of curves. We give families of hyperelliptic curves of genus three, five, six, seven, ten and fifteen whose Jacobians have explicit isogenies (given in terms of correspondences) to other hyperelliptic Jacobians. We describe several families of hyperelliptic curves whose Jacobians have complex or real multiplication; we use correspondences to make the complex and real multiplication explicit, in the form of efficiently computable maps on ideal class representatives. These explicit endomorphisms may be used for efficient integer multiplication on hyperelliptic Jacobians, extending Gallant--Lambert--Vanstone fast multiplication techniques from elliptic curves to higher dimensional Jacobians. We then describe Richelot isogenies for curves of genus two; in contrast to classical treatments of these isogenies, we consider all the Richelot isogenies from a given Jacobian simultaneously. The inter-relationship of Richelot isogenies may be used to deduce information about the endomorphism ring structure of Jacobian surfaces; we conclude with a brief exploration of these techniques.
Cunningham, John B. "Field Testing the Effects of Low Reynolds Number on the Power Performance of the Cal Poly Wind Power Research Center Small Wind Turbine." DigitalCommons@CalPoly, 2020. https://digitalcommons.calpoly.edu/theses/2249.
Full textTyler, Michael Peter. "On the birational section conjecture over function fields." Thesis, University of Exeter, 2017. http://hdl.handle.net/10871/31600.
Full textFerreira, Luan Alberto. "Teoria de corpos de classe e aplicações." Universidade de São Paulo, 2012. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-05122012-102820/.
Full textIn this work, we study the so called \"Class Field Theory\", which give us a simple description of the abelian extension of local and global elds. We also study some applications, like the Kronecker-Weber and Scholz-Reichardt theorems
Weinstein, Madeleine. "Adinkras and Arithmetical Graphs." Scholarship @ Claremont, 2016. http://scholarship.claremont.edu/hmc_theses/85.
Full textSouza, Vera Lúcia Graciani de. "Fatoração de inteiros e grupos sobre conicas." [s.n.], 2009. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306147.
Full textDissertação (mestrado profissional) - Universidade Estadual de Campinas. Instituto de Matematica, Estatistica e Computação Cientifica
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Resumo: Este trabalho tem por objetivo fatorar número inteiro utilizando pontos racionais sobre o círculo unitário. Igualmente pretende determinar alguns grupos sobre cônicas. A pesquisa inicia com os conceitos básicos de Álgebra e Teoria dos Números, que fundamentam que o conjunto de pontos racionais sobre o círculo unitário tem uma estrutura de grupo. Desse conjunto é possível estender a idéia de grupo de pontos racionais sobre o círculo para pontos racionais sobre cônicas. Para encontrar os pontos racionais sobre o círculo foi usada uma parametrização do círculo por funções trigonométricas. Para cada ponto sobre o círculo unitário está associado um ângulo com o eixo positivo das abscissas, portanto adicionar pontos sobre o círculo equivale adicionar seus ângulos correspondentes. Com a operação "adição" de pontos sobre o círculo é possível definir uma estrutura de grupo que é utilizada para fatorar números inteiros. Para a cônica, a operação "adição" é determinada algebricamente ao calcular o coeficiente angular da reta que passa por dois pontos dados e o elemento neutro dessa cônica, também justificada geometricamente. No trabalho foram determinados os grupos de pontos racionais sobre cônicas e demonstrado alguns resultados sobre esses grupos usando os resíduos quadráticos e finalizando com a dedução de alguns resultados sobre a soma das coordenadas dos pontos sobre uma cônica.
Abstract: The objective of this paper is to factorize integer number using rational points on the unitary circle. Also, it intends to determinate some groups on the conics. The research begins with the basic concepts of Algebra and Number Theory ensuring that the rational points set on the unitary circle has a structure of group. From this set is possible to extend the idea of rational points on the circle toward rational points on conics. In order to find the rational points on the circle a parametrization by trigonometric function on it was used. For each point on the unitary circle it is associated an angle with abscissa positive axis, therefore adding points on the circle equals to add its corresponding angles. With the operation of "addition" points on the circle it is possible to define a group structure that is used to factorize integer numbers. For the conic, the "addition" operation is algebraically determinated when the angle coeficient of the line is calculated that joins two given points and the neutral element of that conic, which is geometrically justified. In the research the rational points groups on the conics were determined, and some result on these groups using quadratic residues were demonstrated, and it was finalized with the deduction of some results concerning the coordinates sum of points on a conics.
Mestrado
Mestre em Matemática
Lezowski, Pierre. "Questions d’euclidianité." Thesis, Bordeaux 1, 2012. http://www.theses.fr/2012BOR14642/document.
Full textWe study norm-Euclideanity of number fields and some of its generalizations. In particular, we provide an algorithm to compute the Euclidean minimum of a number field of any signature. This allows us to study the norm-Euclideanity of many number fields. Then, we extend this algorithm to deal with norm-Euclidean classes and we obtain new examples of number fields with a non-principal norm-Euclidean class. Besides, we describe the complete list of pure cubic number fields admitting a norm-Euclidean class. Finally, we study the Euclidean property in quaternion fields. First, we establish its basic properties, then we study some examples. We provide the complete list of Euclidean quaternion fields, which are totally definite over a number field with degree at most two
Gusmão, Ítalo Moraes de Melo. "Números p-ádicos." Universidade Federal da Paraíba, 2015. http://tede.biblioteca.ufpb.br:8080/handle/tede/9337.
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We introduce and de ne the p-adics integer numbers as a result of a search for solutions, for a congruences system that derives from a variable polynomial equation with rational coe cients. We evidence that the p-adic integers set is strictly larger than the integers. We present a criterion so that a rational that holds a correspondent in a p-adic integers set. We search for the possibility to represent irrational and complex numbers as p-adics integers. Algebraically, the p-adic integers set will be an integral domain and, from this, we search for the construction of p-adic integers quotient eld so that shall form the p-adic rationals eld, from a purely algebraically point of view. In the second part, we will expose the bases for the construction of a norm that's di erent from the usual, establishing so a new metric in the rational numbers set and the construction of a non-archimedian eld.
Apresentamos e de nimos os números inteiros p-ádicos como o resultado de uma busca por soluções, para um sistema de congruências, que parte de uma equação polinomial de uma variável, com coe cientes racionais. Constatamos que o conjunto dos inteiros p-ádicos é estritamente maior que os inteiros. Mostramos um critério para que um racional possua um correspondente num conjunto de inteiros p-ádicos. Buscamos a possibilidade de representarmos números irracionais e números complexos como inteiros p-ádicos. Algebricamente, o conjunto dos inteiros p-ádicos será um domínio de integridade e, partindo disto, buscamos a construção de um corpo de frações dos inteiros p-ádicos, que formarão, assim, o corpo dos racionais p-ádicos, de um ponto de vista puramente algébrico. Na segunda parte, vamos expor os fundamentos para a construção de uma norma diferente da habitual, estabelecendo assim uma nova métrica, no conjunto dos números racionais, e a construção de um corpo não-arquimediano.
Villanueva, Gutiérrez José Ibrahim. "Sur quelques questions en théorie d'Iwasawa." Thesis, Bordeaux, 2017. http://www.theses.fr/2017BORD0637/document.
Full textThis work is concerned with the study of logarithmic invariants on $l^{d}$-extensions and is subdivided in three pieces, which are closely related to each other. The first part is a compendium of the different approaches to logarithmic arithmetic, that is the study of the logarithmic invariants. In particular we show the equivalence between the four definitions of the logarithmic class group existing in the literature. Also we give an alternative proof of an Iwasawa logarithmic result. The second part can be thought as an historic addendum on the study of the logarithmic class group over $l$-extensions. Assuming the Gross-Kuz'min conjecture we show that the logarithmic class group can be studied in the Iwasawa setting for non-cyclotomic extensions. We also give relations between the classical $mu$ and $lambda$ invariants and the logarithmic invariants $ilde{mu}$ and $ilde{lambda}$ attached to the logarithmic class groups. The third part studies the properties of the Iwasawa logarithmic module for $l^{d}$-extensions, that is the Galois group $X=Gal(L_{d}/K_{d})$ of the maximal abelian $ell$-extension logarithmically unramified of the compositum $K_{d}$ of the different $l$-extensions of a number field $K$. Assuming the Gross-Kuz'min conjecture we show that $X$ is a noetherian torsion module over the Iwasawa algebra of $K_{d}$. We also deduce relations between the logarithmic invariants $ilde{mu}$ and $ilde{lambda}$ of the $l$-extensions of $K$ which satisfy a splitting condition
Guo, Charng Rang. "On analytic number theory." Thesis, University of Oxford, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.357394.
Full textHarbour, Daniel 1975. "Elements of number theory." Thesis, Massachusetts Institute of Technology, 2003. http://hdl.handle.net/1721.1/17581.
Full textIncludes bibliographical references (leaves 202-205).
The dissertation argues for the necessity of a morphosemantic theory of number, that is, a theory of number serviceable both to semantics and morphology. The basis for this position, and the empirical core of the dissertation, is the relationship between semantically based noun classification and agreement in Kiowa, an indigenous, endangered language of Oklahoma. The central claim is that Universal Grammar provides three number features, concerned with unithood, existence of homogeneous subsets, and properties of those subsets. The features are used to analyze a wide variety of data. Semantic topics include the difference between granular and non-granular mass nouns, collective, non-collective and distributive plurals, and cardinality. Syntactic topics include the structure of DP, noun marking, agreement and suppletion. Morphological topics include the inventory of morphological operations, the featural basis of complex syncretisms, the difference between agreement and suppletion, whether features are privative or binary, and the nature of the Kiowa/Tanoan inverse. Keywords: Kiowa-Tanoan, number, morphology, semantics, agreement, suppletion, inverse, noun class, singular, dual, plural, features, binary, privative.
by Daniel Harbour.
Ph.D.
Ali, T. "String theory and conformal field theory." Thesis, University of Cambridge, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.595446.
Full textBuchanan, Dan Matthews. "Analytic Number Theory and the Prime Number Theorem." Youngstown State University / OhioLINK, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=ysu1525451327211365.
Full textAlkauskas, Giedrius. "Several problems from number theory." Doctoral thesis, Lithuanian Academic Libraries Network (LABT), 2009. http://vddb.library.lt/obj/LT-eLABa-0001:E.02~2009~D_20091008_155751-23469.
Full textDaktaro disertacijoje sprendžiami trys uždaviniai. Pirmasis nagrinėja Minkovskio “klaustuko” funkcijos Stieltjes’o transformacijos (tai yra, šios funkcijos momentų generuojančios funkcijos, taip vadinamosios diadinės periodo funkcijos), analizines savybes ir jos išraišką uždara ar beveik uždara forma. Pagrindinis rezultatas teigia, kad diadinę periodo funkciją galima išreikšti racionaliųjų funkcijų su racionaliaisiais koeficientais konverguojančia eilute. Įrodyme naudojama kompleksinės dinamikos, analizinės grandininių trupmenų teorijos, kelių kompleksinių kintamųjų funkcijų teorijos technika. Antrasis uždavinys nagrinėja funkcines lygtis, susietas su norminėmis ir kitomis kelių kintamųjų formomis. Yra parodoma, kad šios funkcinės lygtys kartais turi kitų, netrivialiųjų sprendinių. Galiausiai, yra pateikiamas naujas mažosios Fermat teoremos įrodymas.
Dyke, Steven Douglas. "Topics in analytic number theory." Thesis, University of Oxford, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.334817.
Full textRowe, Paul Michael Dominic. "Contributions to metric number theory." Thesis, Royal Holloway, University of London, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.408263.
Full textAmirkhanyan, Gagik M. "Problems in combinatorial number theory." Diss., Georgia Institute of Technology, 2014. http://hdl.handle.net/1853/51865.
Full textPowell, Kevin James. "Topics in Analytic Number Theory." BYU ScholarsArchive, 2009. https://scholarsarchive.byu.edu/etd/2084.
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