Relevant bibliographies by topics / Quadrati reciprocity

Academic literature on the topic 'Quadrati reciprocity'

Author: Grafiati
Published: 10 December 2022
Last updated: 28 January 2023

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Journal articles on the topic "Quadrati reciprocity"

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HAMBLETON, S., and V. SCHARASCHKIN. "QUADRATIC RECIPROCITY VIA RESULTANTS." International Journal of Number Theory 06, no. 06 (September 2010): 1413–17. http://dx.doi.org/10.1142/s179304211000354x.

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Rousseau, G. "On the quadratic reciprocity law." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 51, no. 3 (December 1991): 423–25. http://dx.doi.org/10.1017/s1446788700034583.

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AbstractA version of Gauss's fifth proof of the quadratic reciprocity law is given which uses only the simplest group-theoretic considerations (dispensing even with Gauss's Lemma) and makes manifest that the reciprocity law is a simple consequence of the Chinese Remainder Theorem.
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Hambleton, S., and V. Scharaschkin. "Pell conics and quadratic reciprocity." Rocky Mountain Journal of Mathematics 42, no. 1 (February 2012): 91–96. http://dx.doi.org/10.1216/rmj-2012-42-1-91.

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Kronheimer, P. B., M. J. Larsen, and J. Scherk. "Casson's invariant and quadratic reciprocity." Topology 30, no. 3 (November 1991): 335–38. http://dx.doi.org/10.1016/0040-9383(91)90018-y.

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Virgil Barnard. "A Proof of Quadratic Reciprocity." American Mathematical Monthly 122, no. 6 (2015): 588. http://dx.doi.org/10.4169/amer.math.monthly.122.6.588.

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Lemmermeyer, F. "Selmer groups and quadratic reciprocity." Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 76, no. 1 (December 2006): 279–93. http://dx.doi.org/10.1007/bf02960869.

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Perutka, Tomas. "Using decomposition groups to prove theorems about quadratic residues." Journal of the ASB Society 1, no. 1 (December 28, 2020): 12–20. http://dx.doi.org/10.51337/jasb20201228002.

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In this text we elaborate on the modern viewpoint of the quadratic reciprocity law via methods of alge- braic number theory and class field theory. We present original short and simple proofs of so called addi- tional quadratic reciprocity laws and of the multiplicativity of the Legendre symbol using decompositon groups of primes in quadratic and cyclotomic extensions of Q.
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Cox, David A. "Quadratic Reciprocity: Its Conjecture and Application." American Mathematical Monthly 95, no. 5 (May 1988): 442. http://dx.doi.org/10.2307/2322482.

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Duke, William, and Kimberly Hopkins. "Quadratic Reciprocity in a Finite Group." American Mathematical Monthly 112, no. 3 (March 1, 2005): 251. http://dx.doi.org/10.2307/30037441.

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Cox, Darrell, Sourangshu Ghosh, and Eldar Sultanow. "Quadratic, Cubic, Biquadratic, and Quintic Reciprocity." International Journal of Pure and Applied Mathematics Research 2, no. 1 (April 5, 2022): 15–39. http://dx.doi.org/10.51483/ijpamr.2.1.2022.15-39.

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Dissertations / Theses on the topic "Quadrati reciprocity"

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Mittal, Nitish. "Mathematical Reasoning and the Inductive Process: An Examination of The Law of Quadratic Reciprocity." CSUSB ScholarWorks, 2016. https://scholarworks.lib.csusb.edu/etd/282.

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This project investigates the development of four different proofs of the law of quadratic reciprocity, in order to study the critical reasoning process that drives discovery in mathematics. We begin with an examination of the first proof of this law given by Gauss. We then describe Gauss’ fourth proof of this law based on Gauss sums, followed by a look at Eisenstein’s geometric simplification of Gauss’ third proof. Finally, we finish with an examination of one of the modern proofs of this theorem published in 1991 by Rousseau. Through this investigation we aim to analyze the different strategies used in the development of each of these proofs, and in the process gain a better understanding of this theorem.
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Araújo, Leonardo Rodrigues de. "Congruências quadráticas, reciprocidade e aplicações em sala de aula." Universidade Federal da Paraíba, 2013. http://tede.biblioteca.ufpb.br:8080/handle/tede/7480.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
In this study, we evaluate if the congruence x2 a (mod m), where m is prime and (a;m) = 1, has or not solutions, highlighting the importance of Quadratic Residues and consequently the cooperation of the Legendre's Symbol, the Euler's Criterion and the Gauss' Lemma. Also, we demonstrate the Law of Quadratic Reciprocity generalizing situations for composite numbers, that is, the Jacobi's Symbol and its properties. We present some proposals of activities for the High School involving the subject matter and its possible applications, through an understandable language for students of this level.
Neste estudo, vamos avaliar se a congruência x2 a (mod m), onde m é primo e (a;m) = 1, apresenta ou não solução, destacando a importância dos Resíduos Quadráticos e, consequentemente da cooperação do Símbolo de Legendre, do Critério de Euler e do Lema de Gauss. Também, demonstraremos a Lei de Reciprocidade Quadrática generalizando situações para números compostos, ou seja, o Símbolo de Jacobi e suas propriedades. Apresentamos algumas propostas de atividades para o Ensino Médio envolvendo o assunto abordado e suas possíveis aplicações, através de uma linguagem compreensível aos alunos deste nível de ensino.
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Draper, Sandra D. "Evalutaion of certain exponential sums of quadratic functions over a finite fields of odd characteristic." [Tampa, Fla] : University of South Florida, 2006. http://purl.fcla.edu/usf/dc/et/SFE0001674.

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Moore, Benjamin. "Theta Functions, Gauss Sums and Modular Forms." Thesis, 2020. http://hdl.handle.net/2440/125691.

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We present some results related to the areas of theta functions, modular forms, Gauss sums and reciprocity. After a review of background material, we recount the elementary theory of modular forms on congruence subgroups and provide a proof of the transformation law for Jacobi's theta function using special values of zeta functions. We present a new proof, obtained during work with Michael Eastwood, of Jacobi's theorem that every integer is a sum of four squares. Our proof is based on theta functions but emphasises the geometry of the thrice-punctured sphere. Next, we detail some investigations into quadratic Gauss sums. We include a new proof of the Landsberg-Schaar relation by elementary methods, together with a second based on evaluations of Gauss sums. We give elementary proofs of generalised and twisted Landsberg-Schaar relations, and use these results to answer a research problem posed by Berndt, Evans and Williams. We conclude by proving some sextic and octic local analogues of the Landsberg-Schaar relation. Finally, we give yet another proof of the Landsberg-Schaar relation based on the relationship between Mellin transforms and asymptotic expansions. This proof makes clear the relationship between the Landsberg-Schaar relation and the existence of a metaplectic Eisenstein series with certain properties. We note that one may promote this correspondence to the setting of number fields, and furthermore, that the higher theta functions constructed by Banks, Bump and Lieman are ideal candidates for future investigations of such correspondences.
Thesis (MPhil) -- University of Adelaide, School of Mathematical Sciences, 2020
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Books on the topic "Quadrati reciprocity"

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Baumgart, Oswald. The Quadratic Reciprocity Law. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-16283-6.

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Berg, Michael C. The Fourier-Analytic Proof of Quadratic Reciprocity. Hoboken, NJ, USA: John Wiley & Sons, Inc., 2000. http://dx.doi.org/10.1002/9781118032947.

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The Fourier-analytic proof of quadratic reciprocity. New York: John Wiley & Sons, 2000.

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Berg, Michael C. Fourier-Analytic Proof of Quadratic Reciprocity. Wiley & Sons, Incorporated, John, 2011.

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Berg, Michael C. Fourier-Analytic Proof of Quadratic Reciprocity. Wiley & Sons, Incorporated, John, 2011.

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Berg, Michael C. The Fourier-Analytic Proof of Quadratic Reciprocity. Wiley-Interscience, 2000.

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Aka, Menny, Thomas Ward, and Manfred Einsiedler. Journey Through the Realm of Numbers: From Quadratic Equations to Quadratic Reciprocity. Springer International Publishing AG, 2020.

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Lemmermeyer, Franz, and Oswald Baumgart. Quadratic Reciprocity Law: A Collection of Classical Proofs. Springer, 2015.

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Lemmermeyer, Franz, and Oswald Baumgart. The Quadratic Reciprocity Law: A Collection of Classical Proofs. Birkhäuser, 2016.

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The Quadratic Reciprocity Law: A Collection of Classical Proofs. Birkhäuser, 2015.

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Book chapters on the topic "Quadrati reciprocity"

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Ireland, Kenneth, and Michael Rosen. "Quadratic Reciprocity." In A Classical Introduction to Modern Number Theory, 50–65. New York, NY: Springer New York, 1990. http://dx.doi.org/10.1007/978-1-4757-2103-4_5.

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Bressoud, David M. "Quadratic Reciprocity." In Factorization and Primality Testing, 88–101. New York, NY: Springer New York, 1989. http://dx.doi.org/10.1007/978-1-4612-4544-5_7.

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Stein, William. "Quadratic Reciprocity." In Undergraduate Texts in Mathematics, 1–23. New York, NY: Springer New York, 2008. http://dx.doi.org/10.1007/978-0-387-85525-7_4.

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Esmonde, Jody, and M. Ram Murty. "Quadratic Reciprocity." In Problems in Algebraic Number Theory, 239–53. Berlin, Heidelberg: Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/978-3-642-87939-5_17.

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Esmonde, Jody, and M. Ram Murty. "Quadratic Reciprocity." In Problems in Algebraic Number Theory, 81–96. Berlin, Heidelberg: Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/978-3-642-87939-5_7.

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Stillwell, John. "Quadratic reciprocity." In Undergraduate Texts in Mathematics, 158–80. New York, NY: Springer New York, 2003. http://dx.doi.org/10.1007/978-0-387-21735-2_9.

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O’Meara, O. Timothy. "Hilbert’s Reciprocity Law." In Introduction to Quadratic Forms, 190–207. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/978-3-642-62031-7_7.

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Baumgart, Oswald. "From Fermat to Legendre." In The Quadratic Reciprocity Law, 3–6. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-16283-6_1.

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Baumgart, Oswald. "Proofs by Reduction." In The Quadratic Reciprocity Law, 89–105. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-16283-6_10.

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Baumgart, Oswald. "Eisenstein’s Proofs Using Complex Analysis." In The Quadratic Reciprocity Law, 107–9. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-16283-6_11.

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Reports on the topic "Quadrati reciprocity"

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DAI, YANG, ALEXEY B. BORISOV, JAMES W. LONGWORTH, KEITH BOYER, and CHARLES K. RHODES. Quadratic Reciprocity and the Group Orders of Particle States. Office of Scientific and Technical Information (OSTI), June 2001. http://dx.doi.org/10.2172/782710.

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