Relevant bibliographies by topics / Quadrati reciprocity

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Reports

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"

1

HAMBLETON, S., and V. SCHARASCHKIN. "QUADRATIC RECIPROCITY VIA RESULTANTS." International Journal of Number Theory 06, no. 06 (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 (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 (2012): 91–96. http://dx.doi.org/10.1216/rmj-2012-42-1-91.

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4

Kronheimer, P. B., M. J. Larsen, and J. Scherk. "Casson's invariant and quadratic reciprocity." Topology 30, no. 3 (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 (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 (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 (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 (2005): 251. http://dx.doi.org/10.2307/30037441.

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10

Cox, Darrell, Sourangshu Ghosh, and Eldar Sultanow. "Quadratic, Cubic, Biquadratic, and Quintic Reciprocity." International Journal of Pure and Applied Mathematics Research 2, no. 1 (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"

1

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 strateg
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2

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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Submitted by Clebson Anjos (clebson.leandro54@gmail.com) on 2015-05-19T17:19:01Z No. of bitstreams: 1 arquivototal.pdf: 977282 bytes, checksum: 98d2394b44f8e76ed8a9986250386a2c (MD5)<br>Approved for entry into archive by Clebson Anjos (clebson.leandro54@gmail.com) on 2015-05-19T17:19:18Z (GMT) No. of bitstreams: 1 arquivototal.pdf: 977282 bytes, checksum: 98d2394b44f8e76ed8a9986250386a2c (MD5)<br>Made available in DSpace on 2015-05-19T17:19:18Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 977282 bytes, checksum: 98d2394b44f8e76ed8a9986250386a2c (MD5) Previous issue date: 2013-08-13<br>
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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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4

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 investigation
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Books on the topic "Quadrati reciprocity"

1

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

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2

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

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The Fourier-analytic proof of quadratic reciprocity. 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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6

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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8

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

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9

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"

1

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

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2

Bressoud, David M. "Quadratic Reciprocity." In Factorization and Primality Testing. 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. 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. 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. 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. 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. 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. 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. 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. 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"

1

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), 2001. http://dx.doi.org/10.2172/782710.

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