Elliptic and Modular Functions from Gauss to Dedekind to Hecke
eBook - PDF

Elliptic and Modular Functions from Gauss to Dedekind to Hecke

  1. English
  2. PDF
  3. Available on iOS & Android
eBook - PDF

Elliptic and Modular Functions from Gauss to Dedekind to Hecke

About this book

This thorough work presents the fundamental results of modular function theory as developed during the nineteenth and early-twentieth centuries. It features beautiful formulas and derives them using skillful and ingenious manipulations, especially classical methods often overlooked today. Starting with the work of Gauss, Abel, and Jacobi, the book then discusses the attempt by Dedekind to construct a theory of modular functions independent of elliptic functions. The latter part of the book explains how Hurwitz completed this task and includes one of Hurwitz's landmark papers, translated by the author, and delves into the work of Ramanujan, Mordell, and Hecke. For graduate students and experts in modular forms, this book demonstrates the relevance of these original sources and thereby provides the reader with new insights into contemporary work in this area.

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Yes, you can access Elliptic and Modular Functions from Gauss to Dedekind to Hecke by Ranjan Roy in PDF and/or ePUB format, as well as other popular books in Mathematics & History & Philosophy of Mathematics. We have over one million books available in our catalogue for you to explore.

Table of contents

  1. Cover
  2. Half title
  3. Title
  4. Copyright
  5. Contents
  6. Preface
  7. 1 The Basic Modular Forms of the Nineteenth Century
  8. 2 Gauss's Contributions to Modular Forms
  9. 3 Abel and Jacobi on Elliptic Functions
  10. 4 Eisenstein and Hurwitz
  11. 5 Hermite's Transformation of Theta Functions
  12. 6 Complex Variables and Elliptic Functions
  13. 7 Hypergeometric Functions
  14. 8 Dedekind's Paper on Modular Functions
  15. 9 The η Function and Dedekind Sums
  16. 10 Modular Forms and Invariant Theory
  17. 11 The Modular and Multiplier Equations
  18. 12 The Theory of Modular Forms as Reworked by Hurwitz
  19. 13 Ramanujan's Euler Products and Modular Forms
  20. 14 Dirichlet Series and Modular Forms
  21. 15 Sums of Squares
  22. 16 The Hecke Operators
  23. Appendix: Translation of Hurwitz's Paper of 1904
  24. Bibliography
  25. Index