ENGLISH

A First Course in Modular Forms

By Fred Diamond , Jerry Shurman

Book information

Publisher
Springer
Year
2010
ISBN
9781441920058, 1441920056
Language
english
Format
PDF
Filesize
4 MB (3877818 bytes)
Series
Graduate Texts in Mathematics
Edition
1st ed. 2005. Corr. 3nd printing
Pages
447\447
Topic
Mathematics Algebra
Library
kolxoz
Time added
2010-02-18 13:16:04

Description

This book introduces the theory of modular forms, from which all rational elliptic curves arise, with an eye toward the Modularity Theorem. Discussion covers elliptic curves as complex tori and as algebraic curves; modular curves as Riemann surfaces and as algebraic curves; Hecke operators and Atkin-Lehner theory; Hecke eigenforms and their arithmetic properties; the Jacobians of modular curves and the Abelian varieties associated to Hecke eigenforms. As it presents these ideas, the book states the Modularity Theorem in various forms, relating them to each other and touching on their applications to number theory. The authors assume no background in algebraic number theory and algebraic geometry. Exercises are included.

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