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Relevant bibliographies by topics / Gauss sums

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Academic literature on the topic 'Gauss sums'

Author: Grafiati

Published: 4 June 2021

Last updated: 29 January 2023

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Journal articles on the topic "Gauss sums"

1

Shparlinski, Igor E. "Bilinear sums of Gauss sums." Acta Arithmetica 202, no. 4 (2022): 379–88. http://dx.doi.org/10.4064/aa210523-3-2.

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Cohen, Stephen D., Michael Dewar, John B. Friedlander, Daniel Panario, and Igor E. Shparlinski. "Polynomial Gauss sums." Proceedings of the American Mathematical Society 133, no. 8 (2005): 2225–31. http://dx.doi.org/10.1090/s0002-9939-05-08004-4.

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Mbodj, Oumar D. "Quadratic Gauss Sums." Finite Fields and Their Applications 4, no. 4 (1998): 347–61. http://dx.doi.org/10.1006/ffta.1998.0218.

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Cass, Peter, Bruce C. Berndt, Ronald J. Evans, and Kenneth S. Williams. "Gauss and Jacobi Sums." Mathematical Gazette 83, no. 497 (1999): 349. http://dx.doi.org/10.2307/3619097.

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Proskurin, N. V. "On Cubic Exponential Sums and Gauss Sums." Journal of Mathematical Sciences 234, no. 5 (2018): 697–700. http://dx.doi.org/10.1007/s10958-018-4037-0.

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Shparlinski, Igor E. "On sums of Kloosterman and Gauss sums." Transactions of the American Mathematical Society 371, no. 12 (2019): 8679–97. http://dx.doi.org/10.1090/tran/7506.

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Fu, Lei, and Chunlei Liu. "Equidistribution of Gauss sums and Kloosterman sums." Mathematische Zeitschrift 249, no. 2 (2004): 269–81. http://dx.doi.org/10.1007/s00209-004-0696-2.

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Xiaoxue, Li, and Hu Jiayuan. "The hybrid power mean of quartic Gauss sums and Kloosterman sums." Open Mathematics 15, no. 1 (2017): 151–56. http://dx.doi.org/10.1515/math-2017-0014.

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Abstract The main purpose of this paper is using the analytic method and the properties of the classical Gauss sums to study the computational problem of one kind fourth hybrid power mean of the quartic Gauss sums and Kloosterman sums, and give an exact computational formula for it.

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Danas, George. "Note on the quadratic Gauss sums." International Journal of Mathematics and Mathematical Sciences 25, no. 3 (2001): 167–73. http://dx.doi.org/10.1155/s016117120100480x.

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Letpbe an odd prime and{χ(m)=(m/p)},m=0,1,...,p−1be a finite arithmetic sequence with elements the values of a Dirichlet characterχ modpwhich are defined in terms of the Legendre symbol(m/p),(m,p)=1. We study the relation between the Gauss and the quadratic Gauss sums. It is shown that the quadratic Gauss sumsG(k;p)are equal to the Gauss sumsG(k,χ)that correspond to this particular Dirichlet characterχ. Finally, using the above result, we prove that the quadratic Gauss sumsG(k;p),k=0,1,...,p−1are the eigenvalues of the circulantp×pmatrixXwith elements the terms of the sequence{χ(m)}.

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Zhang, Wenpeng, Abdul Samad, and Zhuoyu Chen. "New Identities Dealing with Gauss Sums." Symmetry 12, no. 9 (2020): 1416. http://dx.doi.org/10.3390/sym12091416.

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In this article, we used the elementary methods and the properties of the classical Gauss sums to study the problem of calculating some Gauss sums. In particular, we obtain some interesting calculating formulas for the Gauss sums corresponding to the eight-order and twelve-order characters modulo p, where p be an odd prime with p=8k+1 or p=12k+1.

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Dissertations / Theses on the topic "Gauss sums"

1

Wölk, Sabine [Verfasser]. "Factorization with Gauss sums / Sabine Wölk." München : Verlag Dr. Hut, 2011. http://d-nb.info/1015605028/34.

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Akarsu, Emek Demirci. "Rational points on horocycles and incomplete Gauss sums." Thesis, University of Bristol, 2014. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.652044.

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This thesis studies the connection between the limiting distributions of rational points on horocyle flows and the value distribution of incomplete Gauss sums. A key property of the horocycle flow on a finite-area hyperbolic surface is that long closed horocycles are uniformly distributed. In this thesis we embed rational points on such horocycles on the modular surface and investigate their equidistribution properties. We later extend this study to the metaplectic cover of the modular surface. On the other hand, it is well known that the classical Gauss sums can be evaluated in closed form de

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Alsulmi, Badria. "Generalized Jacobi sums modulo prime powers." Diss., Kansas State University, 2016. http://hdl.handle.net/2097/32668.

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Waara, Einar. "Gauss and Jacobi Sums and the Congruence Zeta Function." Thesis, Uppsala universitet, Analys och sannolikhetsteori, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-354760.

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Petin, Burkhard. "Ein kombinatorisches Beweisverfahren für produktrelationen zwischen Gauss-summen über endlichen kommutativen Ringen." Bonn : [s.n.], 1990. http://catalog.hathitrust.org/api/volumes/oclc/24807249.html.

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Gunawan, Albert. "Gauss's theorem on sums of 3 squares sheaves, and Gauss composition." Thesis, Bordeaux, 2016. http://www.theses.fr/2016BORD0020/document.

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Le théorème de Gauss sur les sommes de 3 carrés relie le nombre de points entiers primitifs sur la sphère de rayon la racine carrée de n au nombre de classes d'un ordre quadratique imaginaire. En 2011, Edixhoven a esquissée une preuve du théorème de Gauss en utilisant une approche de la géométrie arithmétique. Il a utilisé l'action du groupe orthogonal spécial sur la sphère et a donné une bijection entre l'ensemble des SO3(Z)-orbites de tels points, si non vide, avec l'ensemble des classes d'isomorphisme de torseurs sous le stabilisateur. Ce dernier ensemble est un groupe, isomorphe au groupe

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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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Constable, Jonathan A. "Kronecker's Theory of Binary Bilinear Forms with Applications to Representations of Integers as Sums of Three Squares." UKnowledge, 2016. http://uknowledge.uky.edu/math_etds/35.

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In 1883 Leopold Kronecker published a paper containing “a few explanatory remarks” to an earlier paper of his from 1866. His work loosely connected the theory of integral binary bilinear forms to the theory of integral binary quadratic forms. In this dissertation we discover the statements within Kronecker's paper and offer detailed arithmetic proofs. We begin by developing the theory of binary bilinear forms and their automorphs, providing a classification of integral binary bilinear forms up to equivalence, proper equivalence and complete equivalence. In the second chapter we introduce the c

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Fossi, Talom Leopold. "The Quintic Gauss Sums." Doctoral thesis, 2002. http://hdl.handle.net/11858/00-1735-0000-0006-B3BD-8.

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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 investigation

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Books on the topic "Gauss sums"

1

J, Evans Ronald, and Williams Kenneth S, eds. Gauss and Jacobi sums. Wiley, 1998.

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Katz, Nicholas M. Gauss sums, Kloosterman sums, and monodromy groups. Princeton University Press, 1988.

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Fiedler, Thomas. Gauss diagram invariants for knots and links. Kluwer Academic Publishers, 2001.

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Alta.) WIN (Conference) (2nd 2011 Banff. Women in Numbers 2: Research directions in number theory : BIRS Workshop, WIN2 - Women in Numbers 2, November 6-11, 2011, Banff International Research Station, Banff, Alberta, Canada. Edited by David Chantal 1964-, Lalín Matilde 1977-, and Manes Michelle 1970-. American Mathematical Society, 2013.

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5

Williams, Kenneth S., Ronald J. Evans, and Bruce C. Berndt. Gauss and Jacobi Sums. Wiley & Sons, Incorporated, John, 2011.

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Williams, Kenneth S., Ronald J. Evans, and Bruce C. Berndt. Gauss and Jacobi Sums. Wiley & Sons, Incorporated, John, 2011.

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7

Bushnell, C. J., and A. öhlich. Gauss Sums and P-Adic Division Algebras. Springer London, Limited, 2006.

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Katz, Nicholas M. Gauss Sums, Kloosterman Sums, and Monodromy Groups. (AM-116), Volume 116. Princeton University Press, 2016.

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9

Gauss Diagram Invariants for Knots and Links. Springer, 2001.

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Deruelle, Nathalie, and Jean-Philippe Uzan. Waves in a medium. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786399.003.0034.

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This chapter uses a phenomenological approach to obtain a ‘mean’ or macroscopic description of electromagnetic phenomena inside matter. The electromagnetic field inside a medium induces charge and current distributions called polarization. These are the response of the matter to the field. The charge and current densities can be decomposed into the sum of free densities (that is, imposed from outside the medium, and which create the field) and induced densities. The matching conditions on the electromagnetic field at the interface between two different media (for example, a pair of lenses) can

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Book chapters on the topic "Gauss sums"

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Ireland, Kenneth, and Michael Rosen. "Quadratic Gauss Sums." In A Classical Introduction to Modern Number Theory. Springer New York, 1990. http://dx.doi.org/10.1007/978-1-4757-2103-4_6.

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Lemmermeyer, Franz. "Quadratic Gauss Sums." In Springer Undergraduate Mathematics Series. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-78652-6_10.

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Ireland, Kenneth, and Michael Rosen. "Gauss and Jacobi Sums." In A Classical Introduction to Modern Number Theory. Springer New York, 1990. http://dx.doi.org/10.1007/978-1-4757-2103-4_8.

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Lang, Serge. "Gauss Sums as Distributions." In Graduate Texts in Mathematics. Springer New York, 1990. http://dx.doi.org/10.1007/978-1-4612-0987-4_17.

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5

Rubin, Karl. "Kolyvagin’s System of Gauss Sums." In Arithmetic Algebraic Geometry. Birkhäuser Boston, 1991. http://dx.doi.org/10.1007/978-1-4612-0457-2_14.

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Lemmermeyer, Franz. "Power Residues and Gauss Sums." In Springer Monographs in Mathematics. Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/978-3-662-12893-0_4.

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Bilu, Yuri F., Yann Bugeaud, and Maurice Mignotte. "Gauss Sums and Stickelberger’s Theorem." In The Problem of Catalan. Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-10094-4_7.

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Langevin, Philippe, and Patrick Solé. "Gauss Sums over Quasi-Frobenius Rings." In Finite Fields and Applications. Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/978-3-642-56755-1_26.

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Lang, Serge. "The Gamma Function and Gauss Sums." In Graduate Texts in Mathematics. Springer New York, 1990. http://dx.doi.org/10.1007/978-1-4612-0987-4_15.

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Hachenberger, Dirk, and Dieter Jungnickel. "Characters, Gauss Sums, and the DFT." In Topics in Galois Fields. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-60806-4_10.

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Conference papers on the topic "Gauss sums"

1

Schleich, Wolfgang. "Factorization of Numbers and Gauss Sums." In Conference on Coherence and Quantum Optics. OSA, 2007. http://dx.doi.org/10.1364/cqo.2007.cmh2.

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Planat, Michel, and Haret Rosu. "Quantum phase uncertainty in mutually unbiased measurements and Gauss sums." In SPIE Third International Symposium on Fluctuations and Noise, edited by Philip R. Hemmer, Julio R. Gea-Banacloche, Peter Heszler, Sr., and M. Suhail Zubairy. SPIE, 2005. http://dx.doi.org/10.1117/12.608976.

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Ai, XiaoChuan, and XiangKun Ji. "A Note on the Sixth Power Mean Value of the Generalized Quadratic Gauss Sums." In ICVISP 2019: 3rd International Conference on Vision, Image and Signal Processing. ACM, 2019. http://dx.doi.org/10.1145/3387168.3387251.

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Bagci, Cemil. "Banded Doolittle’s Method for the Solutions of Large Systems of Equations." In ASME 1994 International Computers in Engineering Conference and Exhibition and the ASME 1994 8th Annual Database Symposium collocated with the ASME 1994 Design Technical Conferences. American Society of Mechanical Engineers, 1994. http://dx.doi.org/10.1115/cie1994-0454.

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Abstract Doolittle’s method is a much simplified form of Cholesky’s method for solving systems of linear simultaneous equations without inverting the coefficient matrix. In Cholesky’s method the coefficient matrix must be symmetric, the two conjugate triangular matrices must be transposes of each other, and the solution process involves square roots of sums. In Doolittle’s method the coefficient matrix need not be symmetric and there is no constrained relationship between the two conjugate matrices. In this article, Doolittle’s method is used to formulate the banded matrix solution of linear s

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Alvarez Fernandez, Pedro A., Cristian Hernando Acevedo, and Aristide Dogariu. "First-order phase statistics in Laguerre-Gauss speckles." In 2021 IEEE Photonics Society Summer Topicals Meeting Series (SUM). IEEE, 2021. http://dx.doi.org/10.1109/sum48717.2021.9505845.

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Potter, T. E., K. D. Willmert, and M. Sathyamoorthy. "Nonlinear Optimal Design of Dynamic Mechanical Systems." In ASME 1992 Design Technical Conferences. American Society of Mechanical Engineers, 1992. http://dx.doi.org/10.1115/detc1992-0350.

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Abstract Mechanism path generation problems which use link deformations to improve the design lead to optimization problems involving a nonlinear sum-of-squares objective function subjected to a set of linear and nonlinear constraints. Inclusion of the deformation analysis causes the objective function evaluation to be computationally expensive. An optimization method is presented which requires relatively few objective function evaluations. The algorithm, based on the Gauss method for unconstrained problems, is developed as an extension of the Gauss constrained technique for linear constraint

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Vakili, Iman, Mats Gustafsson, and Daniel Sjoberg. "Sum rules for metamaterials in parallel plate waveguides." In 2014 XXXIth URSI General Assembly and Scientific Symposium (URSI GASS). IEEE, 2014. http://dx.doi.org/10.1109/ursigass.2014.6929066.

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Yu, Jyh-Cheng, and Kosuke Ishii. "A Robust Optimization Method for Systems With Significant Nonlinear Effects." In ASME 1993 Design Technical Conferences. American Society of Mechanical Engineers, 1993. http://dx.doi.org/10.1115/detc1993-0325.

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Abstract This paper describes a robust optimization methodology for design involving either complex simulations or actual experiments. The proposed procedure optimizes the worst case response that consists of a weighted sum of expected mean and response variance. The estimation scheme for expected mean and variance adopts the modified 3-point Gauss quadrature integration to assure superior accuracy for systems with significant nonlinear effects. We apply the proposed method to the robust design of geometric parameters of heat treated parts to minimize the cost of post heat treatment operations

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Chen, Ying, and Rodney G. Vaughan. "Sum and difference beam patterns in resonant slotted-waveguide array." In 2017 XXXIInd General Assembly and Scientific Symposium of the International Union of Radio Science (URSI GASS). IEEE, 2017. http://dx.doi.org/10.23919/ursigass.2017.8105241.

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Cayeux, Eric, and Sigmund Stokka. "Buoyancy Force on a Plain or Perforated Portion of a Pipe." In SPE/IADC International Drilling Conference and Exhibition. SPE, 2021. http://dx.doi.org/10.2118/204025-ms.

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Abstract Torque and drag models have been used for many decades to calculate tensions and torques along drill-strings, casing strings and liner strings. However, when applied to sand-screens, it is important to check that all the initial hypotheses used for torque and drag calculations are still valid. In particular, it should be checked whether the buoyancy force on a perforated tube may differ from the one applied to a plain tube. The buoyancy force applied on a pipe, contributes to the sum of efforts at the contact between the pipe and the borehole and therefore influences torque and drag c

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