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Number Theory 3: Iwasawa Theory and Modular Forms(Translations of Mathematical Monographs)

Number Theory 3: Iwasawa Theory and Modular Forms(Translations of Mathematical Monographs)

          
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About the Book

This is the third of three related volumes on number theory. (The first two volumes were also published in the Iwanami Series in Modern Mathematics, as volumes 186 and 240.) The two main topics of this book are Iwasawa theory and modular forms. The presentation of the theory of modular forms starts with several beautiful relations discovered by Ramanujan and leads to a discussion of several important ingredients, including the zeta-regularized products, Kronecker's limit formula, and the Selberg trace formula. The presentation of Iwasawa theory focuses on the Iwasawa main conjecture, which establishes far-reaching relations between a $p$-adic analytic zeta function and a determinant defined from a Galois action on some ideal class groups. This book also contains a short exposition on the arithmetic of elliptic curves and the proof of Fermat's last theorem by Wiles. Together with the first two volumes, this book is a good resource for anyone learning or teaching modern algebraic number theory.

Table of Contents:
Contents Contents for number theory Contents for number theory Preface Preface to the English edition Objectives and outline of these books Modular forms Iwasawa theory Modular forms II Ellliptic curves II Bibliography Answers to questions Answers to exercises Index


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Product Details
  • ISBN-13: 9780821820957
  • Publisher: American Mathematical Society
  • Publisher Imprint: American Mathematical Society
  • Depth: 13
  • Language: English
  • Returnable: Y
  • Spine Width: 15 mm
  • Weight: 280 gr
  • ISBN-10: 0821820958
  • Publisher Date: 30 Oct 2012
  • Binding: Paperback
  • Height: 149 mm
  • No of Pages: 226
  • Series Title: Translations of Mathematical Monographs
  • Sub Title: Iwasawa Theory and Modular Forms
  • Width: 222 mm


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