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Ramanujan's Lost Notebook

Part V

  • George E. Andrews
  • Bruce C. Berndt

Table of contents

  1. Front Matter
    Pages i-xii
  2. George E. Andrews, Bruce C. Berndt
    Pages 1-4
  3. George E. Andrews, Bruce C. Berndt
    Pages 5-16
  4. George E. Andrews, Bruce C. Berndt
    Pages 17-33
  5. George E. Andrews, Bruce C. Berndt
    Pages 35-58
  6. George E. Andrews, Bruce C. Berndt
    Pages 59-76
  7. George E. Andrews, Bruce C. Berndt
    Pages 77-108
  8. George E. Andrews, Bruce C. Berndt
    Pages 109-147
  9. George E. Andrews, Bruce C. Berndt
    Pages 149-183
  10. George E. Andrews, Bruce C. Berndt
    Pages 185-205
  11. George E. Andrews, Bruce C. Berndt
    Pages 207-228
  12. George E. Andrews, Bruce C. Berndt
    Pages 229-248
  13. George E. Andrews, Bruce C. Berndt
    Pages 249-290
  14. George E. Andrews, Bruce C. Berndt
    Pages 291-309
  15. George E. Andrews, Bruce C. Berndt
    Pages 311-320
  16. George E. Andrews, Bruce C. Berndt
    Pages 321-356
  17. George E. Andrews, Bruce C. Berndt
    Pages 357-363
  18. George E. Andrews, Bruce C. Berndt
    Pages 365-372
  19. George E. Andrews, Bruce C. Berndt
    Pages 373-388
  20. George E. Andrews, Bruce C. Berndt
    Pages 389-401
  21. Back Matter
    Pages 403-430

About this book

Introduction

In the spring of 1976, George Andrews of Pennsylvania State University visited the library at Trinity College, Cambridge, to examine the papers of the late G.N. Watson. Among these papers, Andrews discovered a sheaf of 138 pages in the handwriting of Srinivasa Ramanujan. This manuscript was soon designated, "Ramanujan's lost notebook." Its discovery has frequently been deemed the mathematical equivalent of finding Beethoven's tenth symphony.

This fifth and final installment of the authors’ examination of Ramanujan’s lost notebook focuses on the mock theta functions first introduced in Ramanujan’s famous Last Letter. This volume proves all of the assertions about mock theta functions in the lost notebook and in the Last Letter, particularly the celebrated mock theta conjectures. Other topics feature Ramanujan’s many elegant Euler products and the remaining entries on continued fractions not discussed in the preceding volumes. 

Review from the second volume:
"Fans of Ramanujan's mathematics are sure to be delighted by this book. While some of the content is taken directly from published papers, most chapters contain new material and some previously published proofs have been improved. Many entries are just begging for further study and will undoubtedly be inspiring research for decades to come. The next installment in this series is eagerly awaited."
- MathSciNet

Review from the first volume:
"Andrews and Berndt are to be congratulated on the job they are doing. This is the first step...on the way to an understanding of the work of the genius Ramanujan. It should act as an inspiration to future generations of mathematicians to tackle a job that will never be complete."
- Gazette of the Australian Mathematical Society

Keywords

Appell-Lerch Identities Euler products Srinivasa Ramanujan mock theta conjectures mock theta functions partial fraction expansions Ramanujan's Last Letter Appell-Lerch Sums continued fractions lost notebook The Man Who Knew Infinity

Authors and affiliations

  • George E. Andrews
    • 1
  • Bruce C. Berndt
    • 2
  1. 1.Department of MathematicsThe Pennsylvania State UniversityUniversity ParkUSA
  2. 2.Department of MathematicsUniversity of IllinoisUrbanaUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-77834-1
  • Copyright Information Springer International Publishing AG, part of Springer Nature 2018
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-77832-7
  • Online ISBN 978-3-319-77834-1
  • Buy this book on publisher's site