Items related to The Fourier-Analytic Proof of Quadratic Reciprocity
Synopsis
A 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.
"synopsis" may belong to another edition of this title.
About the Author
MICHAEL C. BERG, PhD, is Professor of Mathematics at Loyola Marymount University, Los Angeles, California.
Review
"Provides number theorists interested in analytic methods applied to reciprocity laws with an opportunity to explore the work of Hecke, Weil, and Kubota and their Fourier-analytic treatments..." (SciTech Book News, Vol. 24, No. 4, December 2000)
"The content of the book is very important to number theory and is well-prepared...this book will be found to be very interesting and useful by number theorists in various areas." (Mathematical Reviews, 2002a)
"About this title" may belong to another edition of this title.
- PublisherWiley-Interscience
- Publication date2000
- ISBN 10 0471358304
- ISBN 13 9780471358305
- BindingHardcover
- LanguageEnglish
- Edition number1
- Number of pages128
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Hardcover. Condition: new. Hardcover. A 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 adeles, 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. This unique book explains in a straightforward fashion how quadratic reciprocity relates to some of the most powerful tools of modern number theory such as adeles, metaplectic groups, and representation, demonstrating how this abstract language actually makes sense. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Seller Inventory # 9780471358305
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