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Relevant bibliographies by topics / Number Theory and Field Theory

Academic literature on the topic 'Number Theory and Field Theory'

Author: Grafiati

Published: 4 June 2021

Last updated: 2 February 2022

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Dissertations / Theses
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Journal articles on the topic "Number Theory and Field Theory"

1

Albu, Toma. "Field Theoretic Cogalois Theory via Abstract Cogalois Theory." Journal of Pure and Applied Algebra 208, no. 1 (January 2007): 101–6. http://dx.doi.org/10.1016/j.jpaa.2005.11.008.

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Ikeda, Kâzim Ilhan, and Erol Serbest. "Ramification theory in non-abelian local class field theory." Acta Arithmetica 144, no. 4 (2010): 373–93. http://dx.doi.org/10.4064/aa144-4-4.

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Dunne, Gerald V., and Christian Schubert. "Bernoulli number identities from quantum field theory and topological string theory." Communications in Number Theory and Physics 7, no. 2 (2013): 225–49. http://dx.doi.org/10.4310/cntp.2013.v7.n2.a1.

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Niemi, A. J., and G. W. Semenoff. "Fermion number fractionization in quantum field theory." Physics Reports 135, no. 3 (April 1986): 99–193. http://dx.doi.org/10.1016/0370-1573(86)90167-5.

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Ershov, Yu L. "Local class field theory." St. Petersburg Mathematical Journal 15, no. 06 (November 16, 2004): 837–47. http://dx.doi.org/10.1090/s1061-0022-04-00834-9.

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Hess, Florian, and Maike Massierer. "Tame class field theory for global function fields." Journal of Number Theory 162 (May 2016): 86–115. http://dx.doi.org/10.1016/j.jnt.2015.10.004.

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Saito, Shuji. "Class field theory for curves over local fields." Journal of Number Theory 21, no. 1 (August 1985): 44–80. http://dx.doi.org/10.1016/0022-314x(85)90011-3.

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Poudel, Parashu Ram. "Unified Field Theory." Himalayan Physics 4 (December 23, 2013): 87–90. http://dx.doi.org/10.3126/hj.v4i0.9435.

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Unified field theory is the long-sought means of tying together all known phenomena to explain the nature and behaviour of all matter and energy in existence. The quest for unification has been the perennial theme of modern physics. The belief that all physical phenomena can be reduced to simple and explained by a smaller number of laws is the central tenet of physics. Such a theory could potentially unlock all the secrets of nature and make a myriad of wonders possible, including such benefits as time travel and an inexhaustible source of clean energy, among many others. This paper aims to explain unified theory and its development towards the unification of four interactions in brief.The Himalayan Physics Vol. 4, No. 4, 2013 Page:87-90 Uploaded date: 12/23/2013

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Hiranouchi, Toshiro. "Class field theory for open curves over local fields." Journal de Théorie des Nombres de Bordeaux 30, no. 2 (2018): 501–24. http://dx.doi.org/10.5802/jtnb.1036.

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Miura, Kei, and Hisao Yoshihara. "Field Theory for Function Fields of Plane Quartic Curves." Journal of Algebra 226, no. 1 (April 2000): 283–94. http://dx.doi.org/10.1006/jabr.1999.8173.

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Dissertations / Theses on the topic "Number Theory and Field Theory"

1

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.

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Rakotoniaina, Tahina. "Explicit class field theory for rational function fields." Thesis, Link to the online version, 2008. http://hdl.handle.net/10019/1993.

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Briggs, Matthew Edward. "An Introduction to the General Number Field Sieve." Thesis, Virginia Tech, 1998. http://hdl.handle.net/10919/36618.

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With the proliferation of computers into homes and businesses and the explosive growth rate of the Internet, the ability to conduct secure electronic communications and transactions has become an issue of vital concern. One of the most prominent systems for securing electronic information, known as RSA, relies upon the fact that it is computationally difficult to factor a "large" integer into its component prime integers. If an efficient algorithm is developed that can factor any arbitrarily large integer in a "reasonable" amount of time, the security value of the RSA system would be nullified. The General Number Field Sieve algorithm is the fastest known method for factoring large integers. Research and development of this algorithm within the past five years has facilitated factorizations of integers that were once speculated to require thousands of years of supercomputer time to accomplish. While this method has many unexplored features that merit further research, the complexity of the algorithm prevents almost anyone but an expert from investigating its behavior. We address this concern by first pulling together much of the background information necessary to understand the concepts that are central in the General Number Field Sieve. These concepts are woven together into a cohesive presentation that details each theory while clearly describing how a particular theory fits into the algorithm. Formal proofs from existing literature are recast and illuminated to clarify their inner-workings and the role they play in the whole process. We also present a complete, detailed example of a factorization achieved with the General Number Field Sieve in order to concretize the concepts that are outlined.
Master of Science

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4

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.

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McLeman, Cameron William. "A Golod-Shafarevich Equality and p-Tower Groups." Diss., The University of Arizona, 2008. http://hdl.handle.net/10150/194026.

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Let K be a quadratic imaginary number field, let Kp^(infinity) the top of its p-class field tower for p an odd prime, and let G=Gal(Kp^(infinity)/K). It is known, due to a tremendous collection of work ranging from the principal results of class field theory to the famous Golod-Shafarevich inequality, that G is finite if the p-rank of the class group of K is 0 or 1, and is infinite if this rank is at least 3. This leaves the rank 2 case as the only remaining unsolved case. In this case, while finiteness is still a mystery, much is still known about G: It is a 2-generated, 2-related pro-p-group equipped with an involution that acts as the inverse modulo commutators, and is of one of three possible Zassenhaus types (defined in the paper). If such a group is finite, we will call it an interesting p-tower group. We further the knowledge on such groups by showing that one particular Zassenhaus type can occur as an interesting p-tower group only if the group has order at least p^24 (Proposition 8.1), and by proving a succinct cohomological condition (Proposition 4.7) for a p-tower group to be infinite. More generally, we prove a Golod-Shafarevich equality (Theorem 5.2), refining the famous Golod-Shafarevich inequality, and obtaining as a corollary a strict strengthening of previous Golod-Shafarevich inequalities (Corollary 5.5). Of interest is that this equality applies not only to finite p-groups but also to p-adic analytic pro-p-groups, a class of groups of particular relevance due to their prominent appearance in the Fontaine-Mazur conjecture. This refined version admits as a consequence that the sizes of the first few modular dimension subgroups of an interesting p-tower group G are completely determined by p and its Zassenhaus type, and we compute these sizes. As another application, we prove a new formula (Corollary 5.3) for the Fp-dimensions of the successive quotients of dimension subgroups of free pro-p-groups.

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Solomon, 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.

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Swanson, Colleen M. "Algebraic number fields and codes /." Connect to online version, 2006. http://ada.mtholyoke.edu/setr/websrc/pdfs/www/2006/172.pdf.

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Bamunoba, Alex Samuel. "Cyclotomic polynomials (in the parallel worlds of number theory)." Thesis, Stellenbosch : Stellenbosch University, 2011. http://hdl.handle.net/10019.1/17865.

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Thesis (MSc)--Stellenbosch University, 2011.
ENGLISH 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).

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Cipra, James Arthur. "Waring’s number in finite fields." Diss., Kansas State University, 2010. http://hdl.handle.net/2097/4152.

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Doctor of Philosophy
Department 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 $\gamma(k,p^2)\le16\sqrt{k+1}$.

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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.

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Books on the topic "Number Theory and Field Theory"

1

Weil, André. Basic number theory. Berlin: Springer, 1995.

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Lang, Serge. Algebraic number theory. 2nd ed. New York: Springer-Verlag, 1994.

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Lang, Serge. Algebraic number theory. New York: Springer-Verlag, 1986.

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Janusz, Gerald J. Algebraic number fields. 2nd ed. Providence, R.I: American Mathematical Society, 1996.

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Fried, Michael D. Field arithmetic. 2nd ed. Berlin: Springer, 2005.

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1942-, Jarden Moshe, ed. Field arithmetic. Berlin: Springer-Verlag, 1986.

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1942-, Jarden Moshe, ed. Field arithmetic. 3rd ed. Berlin: Springer, 2008.

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Number theory in function fields. New York: Springer, 2001.

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Borwein, Jonathan M., Igor Shparlinski, and Wadim Zudilin, eds. Number Theory and Related Fields. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-6642-0.

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Rosen, Michael. Number Theory in Function Fields. New York, NY: Springer New York, 2002. http://dx.doi.org/10.1007/978-1-4757-6046-0.

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Book chapters on the topic "Number Theory and Field Theory"

1

Koch, H. "Class Field Theory." In Algebraic Number Theory, 90–150. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/978-3-642-58095-6_2.

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Vasquez, A. T. "Rational Desingularization of a Curve Defined Over a Finite Field." In Number Theory, 229–50. New York, NY: Springer New York, 1991. http://dx.doi.org/10.1007/978-1-4757-4158-2_12.

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Yui, Noriko. "The brauer group of the product of two curves over a finite field." In Number Theory, 254–83. Berlin, Heidelberg: Springer Berlin Heidelberg, 1985. http://dx.doi.org/10.1007/bfb0074609.

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Zimmermann, W. "Reduction in the Number of Coupling Parameters." In Quantum Field Theory, 211–25. Berlin, Heidelberg: Springer Berlin Heidelberg, 1985. http://dx.doi.org/10.1007/978-3-642-70307-2_13.

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Cohen, Henri. "Computational Class Field Theory." In Advanced Topics in Computional Number Theory, 163–222. New York, NY: Springer New York, 2000. http://dx.doi.org/10.1007/978-1-4419-8489-0_4.

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Todorov, Ivan. "Perturbative Quantum Field Theory Meets Number Theory." In Springer Proceedings in Mathematics & Statistics, 1–28. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-37031-2_1.

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Kleiman, Howard. "On NTU’S in Function Fields." In Number Theory, 219–20. New York, NY: Springer New York, 2004. http://dx.doi.org/10.1007/978-1-4419-9060-0_13.

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Hriljac, Paul. "Splitting fields of principal homogeneous spaces." In Number Theory, 214–29. Berlin, Heidelberg: Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/bfb0072982.

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Kaltofen, Erich, and Noriko Yui. "Explicit Construction of the Hilbert Class Fields of Imaginary Quadratic Fields by Integer Lattice Reduction." In Number Theory, 149–202. New York, NY: Springer New York, 1991. http://dx.doi.org/10.1007/978-1-4757-4158-2_8.

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Jensen, Erik, and M. Ram Murty. "Artin’s Conjecture for Polynomials Over Finite Fields." In Number Theory, 167–81. Basel: Birkhäuser Basel, 2000. http://dx.doi.org/10.1007/978-3-0348-7023-8_10.

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Conference papers on the topic "Number Theory and Field Theory"

1

Hietanen, Ari. "Quark number susceptibility of high temperature QCD." In XXIVth International Symposium on Lattice Field Theory. Trieste, Italy: Sissa Medialab, 2006. http://dx.doi.org/10.22323/1.032.0137.

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Panzer, Erik, Thomas Bitoun, Christian Bogner, and René Pascal Klausen. "The number of master integrals as Euler characteristic." In Loops and Legs in Quantum Field Theory. Trieste, Italy: Sissa Medialab, 2018. http://dx.doi.org/10.22323/1.303.0065.

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Velytsky, Alexander. "Quark number fluctuations at high temperatures." In The XXVII International Symposium on Lattice Field Theory. Trieste, Italy: Sissa Medialab, 2010. http://dx.doi.org/10.22323/1.091.0159.

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Giudice, Pietro, Simon Hands, and Jon-Ivar Skullerud. "Quark number susceptibility at finite density and low temperature." In XXIX International Symposium on Lattice Field Theory. Trieste, Italy: Sissa Medialab, 2012. http://dx.doi.org/10.22323/1.139.0193.

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Hegde, Prasad. "Quark Number Susceptibilities with Domain-Wall Fermions." In The XXVI International Symposium on Lattice Field Theory. Trieste, Italy: Sissa Medialab, 2009. http://dx.doi.org/10.22323/1.066.0187.

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Patel, Apoorva. "Baryon Number Correlation Signals in Heavy Ion Collisions." In The 30th International Symposium on Lattice Field Theory. Trieste, Italy: Sissa Medialab, 2012. http://dx.doi.org/10.22323/1.164.0096.

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Petreczky, Peter. "Quark number susceptibilities at high temperatures." In 31st International Symposium on Lattice Field Theory LATTICE 2013. Trieste, Italy: Sissa Medialab, 2014. http://dx.doi.org/10.22323/1.187.0158.

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Meng, Xiangfei, Anyi Li, Andrei Alexandru, and Keh-Fei Liu. "Winding number expansion in canonical approach to finite density." In The XXVI International Symposium on Lattice Field Theory. Trieste, Italy: Sissa Medialab, 2009. http://dx.doi.org/10.22323/1.066.0032.

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Gavai, Rajiv V., and Sayantan Sharma. "On curing the divergences in the quark number susceptibility." In The 32nd International Symposium on Lattice Field Theory. Trieste, Italy: Sissa Medialab, 2015. http://dx.doi.org/10.22323/1.214.0189.

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Hietanen, Ari, and Kari Rummukainen. "Quark number susceptibility of high temperature and finite density QCD." In The XXV International Symposium on Lattice Field Theory. Trieste, Italy: Sissa Medialab, 2008. http://dx.doi.org/10.22323/1.042.0192.

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Reports on the topic "Number Theory and Field Theory"

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Koroteev, Peter. Morse Theory in Field Theory. GIQ, 2012. http://dx.doi.org/10.7546/giq-8-2007-207-220.

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Fisher, Michael, Mike Bardzell, and Kurt Ludwick. PascGalois Number Theory Classroom Resources. Washington, DC: The MAA Mathematical Sciences Digital Library, July 2008. http://dx.doi.org/10.4169/loci002637.

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Morariu, Bogdan. Noncommutative Geometry in M-Theory and Conformal Field Theory. Office of Scientific and Technical Information (OSTI), May 1999. http://dx.doi.org/10.2172/760324.

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Hotes, S. A. Understanding conformal field theory through parafermions and Chern Simons theory. Office of Scientific and Technical Information (OSTI), November 1992. http://dx.doi.org/10.2172/6653388.

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Hotes, Scott A. Understanding conformal field theory through parafermions and Chern Simons theory. Office of Scientific and Technical Information (OSTI), November 1992. http://dx.doi.org/10.2172/10140828.

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Jaffe, Arthur M. "Quantum Field Theory and QCD". Office of Scientific and Technical Information (OSTI), February 2006. http://dx.doi.org/10.2172/891184.

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Caldi, D. G. Studies in quantum field theory. Office of Scientific and Technical Information (OSTI), March 1993. http://dx.doi.org/10.2172/10165764.

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Steinhauer, L. C. Theory of field reversed configurations. Office of Scientific and Technical Information (OSTI), January 1990. http://dx.doi.org/10.2172/5072539.

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Henyey, Frank S. Internal Wave Theory, Modeling and Theory of the Internal Wave Field. Fort Belvoir, VA: Defense Technical Information Center, April 1995. http://dx.doi.org/10.21236/ada300337.

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Dunne, Gerald V., Thomas Blum, and Alexander Kovner. Investigations in Particle and Field Theory. Office of Scientific and Technical Information (OSTI), October 2013. http://dx.doi.org/10.2172/1095923.

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