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Other titles in the Pure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs and Tracts series:

The Fourier-Analytic Proof of Quadratic Reciprocity (Pure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs and Tracts)

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The Fourier-Analytic Proof of Quadratic Reciprocity (Pure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs and Tracts) Cover

 

Synopses & Reviews

Publisher Comments:

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 ad?les, 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.

Book News Annotation:

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 of quadratic reciprocity. Shows how Weil's ground-breaking representation-theoretic treatment is equivalent to Hecke's classical approach, then presents Kubota's algebraic reformulation of the Hecke-Weil proof. Concludes that the critical common factor among the three proofs is Poisson summation. Includes extensive commutative diagrams for comparing the Weil and Kubota architectures. Berg is professor of mathematics at Loyola Marymount University.
Annotation c. Book News, Inc., Portland, OR (booknews.com)

Synopsis:

The author clearly demonstrates the value of the analytic approach, incorporating some of the most powerful tools of modern number theory, including adles, 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:

Der relativ einfache quadratische Fall wurde zuerst 1923 von Hecke gelöst, dann 1964 von Weil in die Darstellung mit unitären Gruppen übertragen. Der analytische Beweis des allgemeinen Falls n-ter Ordnung steht bis heute noch aus. Beiträge etlicher Zahlentheoretiker zum Problem der Reziprozitätsgesetze faßt der Autor dieses Buch zusammen, diskutiert sie verallgemeinernd und zeigt Ansätze zur Lösung des Hecke-Problems auf. (08/00)

Synopsis:

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.

Description:

Includes bibliographical references (p. 109-112) and index.

About the Author

MICHAEL C. BERG, PhD, is Professor of Mathematics at Loyola Marymount University, Los Angeles, California.

Table of Contents

Hecke's Proof of Quadratic Reciprocity.

Two Equivalent Forms of Quadratic Reciprocity.

The Stone-Von Neumann Theorem.

Weil's "Acta" Paper.

Kubota and Cohomology.

The Algebraic Agreement Between the Formalisms of Weil and Kubota.

Hecke's Challenge: General Reciprocity and Fourier Analysis on the March.

Bibliography.

Index.

Product Details

ISBN:
9780471358305
Author:
Berg, Michael C.
Publisher:
Wiley-Interscience
Author:
Berg, Weger Marl
Location:
New York :
Subject:
Number Theory
Subject:
Equations, quartic
Subject:
Reciprocity theorems
Subject:
Mathematics-Number Theory
Copyright:
Edition Description:
WOL online Book (not BRO)
Series:
Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts
Series Volume:
41
Publication Date:
20110314
Binding:
HARDCOVER
Grade Level:
General/trade
Language:
English
Illustrations:
Yes
Pages:
118
Dimensions:
242 x 162 x 16 mm 14 oz

Related Subjects

Science and Mathematics » Mathematics » General
Science and Mathematics » Mathematics » Number Theory

The Fourier-Analytic Proof of Quadratic Reciprocity (Pure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs and Tracts) New Hardcover
0 stars - 0 reviews
$199.95 In Stock
Product details 118 pages Wiley-Interscience - English 9780471358305 Reviews:
"Synopsis" by , The author clearly demonstrates the value of the analytic approach, incorporating some of the most powerful tools of modern number theory, including adles, 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" by , Der relativ einfache quadratische Fall wurde zuerst 1923 von Hecke gelöst, dann 1964 von Weil in die Darstellung mit unitären Gruppen übertragen. Der analytische Beweis des allgemeinen Falls n-ter Ordnung steht bis heute noch aus. Beiträge etlicher Zahlentheoretiker zum Problem der Reziprozitätsgesetze faßt der Autor dieses Buch zusammen, diskutiert sie verallgemeinernd und zeigt Ansätze zur Lösung des Hecke-Problems auf. (08/00)
"Synopsis" by , 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.
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