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Ramanujan's Lost Notebook

Part IV

  • George E. Andrews
  • Bruce C. Berndt

Table of contents

  1. Front Matter
    Pages i-xvii
  2. George E. Andrews, Bruce C. Berndt
    Pages 1-5
  3. George E. Andrews, Bruce C. Berndt
    Pages 7-91
  4. George E. Andrews, Bruce C. Berndt
    Pages 93-109
  5. George E. Andrews, Bruce C. Berndt
    Pages 111-130
  6. George E. Andrews, Bruce C. Berndt
    Pages 131-151
  7. George E. Andrews, Bruce C. Berndt
    Pages 153-162
  8. George E. Andrews, Bruce C. Berndt
    Pages 163-181
  9. George E. Andrews, Bruce C. Berndt
    Pages 183-212
  10. George E. Andrews, Bruce C. Berndt
    Pages 213-237
  11. George E. Andrews, Bruce C. Berndt
    Pages 239-250
  12. George E. Andrews, Bruce C. Berndt
    Pages 251-264
  13. George E. Andrews, Bruce C. Berndt
    Pages 265-284
  14. George E. Andrews, Bruce C. Berndt
    Pages 285-305
  15. George E. Andrews, Bruce C. Berndt
    Pages 307-327
  16. George E. Andrews, Bruce C. Berndt
    Pages 329-350
  17. George E. Andrews, Bruce C. Berndt
    Pages 377-391
  18. George E. Andrews, Bruce C. Berndt
    Pages 393-406
  19. George E. Andrews, Bruce C. Berndt
    Pages 407-412
  20. Back Matter
    Pages 413-439

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 volume is the fourth of five volumes that the authors plan to write on Ramanujan’s lost notebook.​ In contrast to the first three books on Ramanujan's Lost Notebook, the fourth book does not focus on q-series.  Most of the entries examined in this volume fall under the purviews of number theory and classical analysis.  Several incomplete manuscripts of Ramanujan published by Narosa with the lost notebook are discussed.  Three of the partial manuscripts are on diophantine approximation, and others are in classical Fourier analysis and prime number theory.   Most of the entries in number theory fall under the umbrella of classical analytic number theory.   Perhaps the most intriguing entries are connected with the classical, unsolved circle and divisor problems.

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

Bessel Functions Euler's constant Fourier transforms Guinand's Formula Koshliakov's Formula Mellin transforms circle and divisor problems classical analysis classical analytic number theory diophantine approximation divisor sums gamma function hypergeometric functions prime number theorem transformation formulas trigonometric series

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

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