A first course in modular forms

Author(s)

Bibliographic Information

A first course in modular forms

Fred Diamond, Jerry Shurman

(Graduate texts in mathematics, 228)

Springer, c2005

[new printing]

Available at  / 14 libraries

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Note

Preface: p. xi-xvi

List of symbols: p. [423]-428

Index: p. [429]-433

Bibliographical references: p. [435]-438

Description and Table of Contents

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.

Table of Contents

Modular Forms, Elliptic Curves, and Modular Curves.- Modular Curves as Riemann Surfaces.- Dimension Formulas.- Eisenstein Series.- Hecke Operators.- Jacobians and Abelian Varieties.- Modular Curves as Algebraic Curves.- The Eichler-Shimura Relation and L-functions.- Galois Representations.

by "Nielsen BookData"

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Details

  • NCID
    BA83513083
  • ISBN
    • 9780387232294
  • LCCN
    2004058971
  • Country Code
    us
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Place of Publication
    New York
  • Pages/Volumes
    xvi, 438 p.
  • Size
    25 cm
  • Classification
  • Subject Headings
  • Parent Bibliography ID
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