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Introduction to Modular Forms

  • Book
  • © 1987

Overview

Authors:
  1. Serge Lang

    1. Department of Mathematics, Yale University, New Haven, USA

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Part of the book series: Grundlehren der mathematischen Wissenschaften (GL, volume 222)

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Table of contents (15 chapters)

  1. Front Matter

    Pages i-ix
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  2. Classical Theory

    1. Front Matter

      Pages 1-1
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    2. Modular Forms

      • Serge Lang
      Pages 3-15

    3. Hecke Operators

      • Serge Lang
      Pages 16-23

    4. The Petersson Scalar Product

      • Serge Lang
      Pages 24-43

  3. Periods of Cusp Forms

    1. Front Matter

      Pages N1-N1
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    2. Modular Symbols

      • Serge Lang
      Pages 57-67

    3. Coefficients and Periods of Cusp Forms on SL2(Z)

      • Serge Lang
      Pages 68-83

    4. The Eichler-Shimura Isomorphism on SL2(Z)

      • Serge Lang
      Pages 84-98

  4. Modular Forms for Congruence Subgroups

    1. Front Matter

      Pages 99-99
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    2. Higher Levels

      • Serge Lang
      Pages 101-117

    3. Atkin-Lehner Theory

      • Serge Lang
      Pages 118-137

    4. The Dedekind Formalism

      • Serge Lang
      Pages 138-147

  5. Congruence Properties and Galois Representations

    1. Front Matter

      Pages 149-149
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    2. Congruences and Reduction mod p

      • Serge Lang
      Pages 151-175

    3. Galois Representations

      • Serge Lang
      Pages 176-203

  6. p-Adic Distributions

    1. Front Matter

      Pages 205-205
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    2. General Distributions

      • Serge Lang
      Pages 207-227

    3. Bernoulli Numbers and Polynomials

      • Serge Lang
      Pages 228-239

    4. The Complex L-Functions

      • Serge Lang
      Pages 240-246
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Keywords

About this book

From the reviews: "This book gives a thorough introduction to several theories that are fundamental to research on modular forms. Most of the material, despite its importance, had previously been unavailable in textbook form. Complete and readable proofs are given... In conclusion, this book is a welcome addition to the literature for the growing number of students and mathematicians in other fields who want to understand the recent developments in the theory of modular forms."
#Mathematical Reviews#
"This book will certainly be indispensable to all those wishing to get an up-to-date initiation to the theory of modular forms."
#Publicationes Mathematicae#

Reviews

From the reviews: "This book gives a thorough introduction to several theories that are fundamental to research on modular forms. Most of the material, despite its importance, had previously been unavailable in textbook form. Complete and readable proofs are given... In conclusion, this book is a welcome addition to the literature for the growing number of students and mathematicians in other fields who want to understand the recent developments in the theory of modular forms." #Mathematical Reviews# "This book will certainly be indispensable to all those wishing to get an up-to-date initiation to the theory of modular forms." #Publicationes Mathematicae#

Authors and Affiliations

  • Department of Mathematics, Yale University, New Haven, USA

    Serge Lang

Bibliographic Information

  • Book Title: Introduction to Modular Forms

  • Authors: Serge Lang

  • Series Title: Grundlehren der mathematischen Wissenschaften

  • DOI: https://doi.org/10.1007/978-3-642-51447-0

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1987

  • Hardcover ISBN: 978-3-540-07833-3Published: 01 December 1976

  • Softcover ISBN: 978-3-642-05716-8Published: 19 October 2010

  • eBook ISBN: 978-3-642-51447-0Published: 06 December 2012

  • Series ISSN: 0072-7830

  • Series E-ISSN: 2196-9701

  • Edition Number: 1

  • Number of Pages: IX, 265

  • Topics: Number Theory, Analysis, Algebraic Geometry

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