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OverviewA unique synthesis of the three existing Fourier-analytic treatments of quadratic reciprocity. The relative quadratic case was first settled by Hecke in 1923, then recast by Weil in 1964 into the language of unitary group representations. The analytic proof of the general n-th order case is still an open problem today, going back to the end of Hecke's famous treatise of 1923. The Fourier-Analytic Proof of Quadratic Reciprocity provides number theorists interested in analytic methods applied to reciprocity laws with a unique opportunity to explore the works of Hecke, Weil, and Kubota. This work brings together for the first time in a single volume the three existing formulations of the Fourier-analytic proof of quadratic reciprocity. It shows how Weil's groundbreaking representation-theoretic treatment is in fact equivalent to Hecke's classical approach, then goes a step further, presenting Kubota's algebraic reformulation of the Hecke-Weil proof. Extensive commutative diagrams for comparing the Weil and Kubota architectures are also featured. The author clearly demonstrates the value of the analytic approach, incorporating some of the most powerful tools of modern number theory, including adèles, metaplectric groups, and representations. Finally, he points out that the critical common factor among the three proofs is Poisson summation, whose generalization may ultimately provide the resolution for Hecke's open problem. Full Product DetailsAuthor: Michael C. Berg (Loyola Marymount University)Publisher: John Wiley & Sons Inc Imprint: Wiley-Interscience Dimensions: Width: 16.20cm , Height: 1.60cm , Length: 24.20cm Weight: 0.397kg ISBN: 9780471358305ISBN 10: 0471358304 Pages: 118 Publication Date: 29 February 2000 Audience: College/higher education , Professional and scholarly , Undergraduate , Postgraduate, Research & Scholarly Format: Hardback Publisher's Status: Active Availability: Out of stock  The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available. Table of ContentsReviewsProvides number theorists interested in analytic methods applied to reciprocity laws...explore the work of Hecke, Weil, and Kubota and their Fourier-analytic treatments... (SciTech Book News, Vol. 24, No. 4, December 2000) For anyone interested in the unsolved problem of proving reciprocity laws via Fourier analysis. (American Mathematical Monthly, March 2002) Provides number theorists interested in analytic methods applied to reciprocity laws...explore the work of Hecke, Weil, and Kubota and their Fourier--analytic treatments... (SciTech Book News, Vol. 24, No. 4, December 2000) Author InformationMICHAEL C. BERG, PhD, is Professor of Mathematics at Loyola Marymount University, Los Angeles, California. Tab Content 6Author Website:Countries AvailableAll regions |
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