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Problems in the Theory of Modular Forms

  • M. Ram Murty
  • Michael Dewar
  • Hester Graves

Part of the HBA Lecture Notes in Mathematics book series (HBALNM)

Also part of the IMSc Lecture Notes in Mathematics book sub series (IMSLNM)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Problems

    1. Front Matter
      Pages 1-1
    2. M. Ram Murty, Michael Dewar, Hester Graves
      Pages 3-14
    3. M. Ram Murty, Michael Dewar, Hester Graves
      Pages 15-23
    4. M. Ram Murty, Michael Dewar, Hester Graves
      Pages 25-33
    5. M. Ram Murty, Michael Dewar, Hester Graves
      Pages 35-52
    6. M. Ram Murty, Michael Dewar, Hester Graves
      Pages 53-71
    7. M. Ram Murty, Michael Dewar, Hester Graves
      Pages 73-83
    8. M. Ram Murty, Michael Dewar, Hester Graves
      Pages 85-94
    9. M. Ram Murty, Michael Dewar, Hester Graves
      Pages 95-103
    10. M. Ram Murty, Michael Dewar, Hester Graves
      Pages 105-133
    11. M. Ram Murty, Michael Dewar, Hester Graves
      Pages 135-150
  3. Solutions

    1. Front Matter
      Pages 151-151
    2. M. Ram Murty, Michael Dewar, Hester Graves
      Pages 153-160
    3. M. Ram Murty, Michael Dewar, Hester Graves
      Pages 161-174
    4. M. Ram Murty, Michael Dewar, Hester Graves
      Pages 175-183
    5. M. Ram Murty, Michael Dewar, Hester Graves
      Pages 185-197
    6. M. Ram Murty, Michael Dewar, Hester Graves
      Pages 199-216
    7. M. Ram Murty, Michael Dewar, Hester Graves
      Pages 217-230
    8. M. Ram Murty, Michael Dewar, Hester Graves
      Pages 231-238
    9. M. Ram Murty, Michael Dewar, Hester Graves
      Pages 239-243
    10. M. Ram Murty, Michael Dewar, Hester Graves
      Pages 245-268
    11. M. Ram Murty, Michael Dewar, Hester Graves
      Pages 269-283
  4. Back Matter
    Pages 285-291

About this book

Introduction

This book introduces the reader to the fascinating world of modular forms through a problem-solving approach. As such, besides researchers, the book can be used by the undergraduate and graduate students for self-instruction. The topics covered include q-series, the modular group, the upper half-plane, modular forms of level one and higher level, the Ramanujan τ-function, the Petersson inner product, Hecke operators, Dirichlet series attached to modular forms and further special topics. It can be viewed as a gentle introduction for a deeper study of the subject. Thus, it is ideal for non-experts seeking an entry into the field.  

 

Keywords

q-series Modular Group Hecke subgroups Fundamental domains Poincar´e metric Fourier expansions valence formula Ramanujan congruences Nebentypus

Authors and affiliations

  • M. Ram Murty
    • 1
  • Michael Dewar
    • 2
  • Hester Graves
    • 3
  1. 1.Dept of Math & Statistics, JefferyQueen's University Dept of Math & Statistics, JefferyKingstonCanada
  2. 2.Queen’s University KingstonCanada
  3. 3.500 S State StUniversity of Michigan 500 S State StAnn ArborUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-981-10-2651-5
  • Copyright Information Springer Science+Business Media Singapore 2016 and Hindustan Book Agency 2016 2016
  • Publisher Name Springer, Singapore
  • eBook Packages Mathematics and Statistics
  • Online ISBN 978-981-10-2651-5
  • Series Print ISSN 2509-8063
  • Series Online ISSN 2509-8071
  • Buy this book on publisher's site