ENGLISH

Number Theory 3: Iwasawa Theory and Modular Forms

By Nobushige Kurokawa , Takeshi Saito , Masato Kurihara

Book information

Publisher
American Mathematical Society
Year
2012
ISBN
0821820958, 9780821820957
Language
english
Format
PDF
Filesize
7 MB (7615831 bytes)
Series
Translations of Mathematical Monographs
Pages
226\242
DPI
600
Scanned
yes
Time added
2016-05-22 16:16:17
Language & Grammar;WritingReference;Almanacs & Yearbooks;Atlases & Maps;CareResearch & Publishing Guides;Number Theory;Pure Ma

Description

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.

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