The Fourier-Analytic Proof of Quadratic Reciprocity PDF
By:Berg,Michael C. Berg
Published on 2000-03-03 by John Wiley & Sons
A unique synthesis of the three existing Fourier-analytictreatments 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 grouprepresentations. The analytic proof of the general n-th order caseis still an open problem today, going back to the end of Hecke'sfamous treatise of 1923. The Fourier-Analytic Proof of QuadraticReciprocity provides number theorists interested in analyticmethods applied to reciprocity laws with a unique opportunity toexplore the works of Hecke, Weil, and Kubota. This work brings together for the first time in a single volume thethree existing formulations of the Fourier-analytic proof ofquadratic reciprocity. It shows how Weil's groundbreakingrepresentation-theoretic treatment is in fact equivalent to Hecke'sclassical approach, then goes a step further, presenting Kubota'salgebraic reformulation of the Hecke-Weil proof. Extensivecommutative diagrams for comparing the Weil and Kubotaarchitectures are also featured. The author clearly demonstrates the value of the analytic approach,incorporating some of the most powerful tools of modern numbertheory, including adèles, metaplectric groups, andrepresentations. Finally, he points out that the critical commonfactor among the three proofs is Poisson summation, whosegeneralization may ultimately provide the resolution for Hecke'sopen problem.
This Book was ranked at 24 by Google Books for keyword Analytic.
Book ID of The Fourier-Analytic Proof of Quadratic Reciprocity's Books is fxVZybOHF8EC, Book which was written byBerg,Michael C. Berghave ETAG "L2MsF8ClT6c"
Book which was published by John Wiley & Sons since 2000-03-03 have ISBNs, ISBN 13 Code is 9780471358305 and ISBN 10 Code is 0471358304
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