Ramanujan's Lost Notebook

Part IV

Authors: Andrews, George E, Berndt, Bruce C.

  • Fourth volume of a series of five volumes including some of Ramanujan's deepest work in the last year of his life
  • Contains material of which mathematicians currently lack a complete understanding
  • Focuses on claims in classical analysis and classical analytic number theory found in "The Lost Notebook and Other Unpublished Papers"
  • Two key results show that Ramanujan had a strong interest in the classical circle and divisor problems
  • Although Ramanujan never published any papers in diophantine approximation, three of the partial manuscripts are on this subject
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About this book

​​​​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​

About the authors

George E. Andrews is currently a professor of mathematics at Pennsylvania State University. Bruce C. Berndt is currently a professor of mathematics at the University of Illinois.

Table of contents (21 chapters)

  • Introduction

    Andrews, George E. (et al.)

    Pages 1-5

  • Double Series of Bessel Functions and the Circle and Divisor Problems

    Andrews, George E. (et al.)

    Pages 7-91

  • Koshliakov’s Formula and Guinand’s Formula

    Andrews, George E. (et al.)

    Pages 93-109

  • Theorems Featuring the Gamma Function

    Andrews, George E. (et al.)

    Pages 111-130

  • Hypergeometric Series

    Andrews, George E. (et al.)

    Pages 131-151

Buy this book

eBook $109.00
price for USA (gross)
  • ISBN 978-1-4614-4081-9
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $149.00
price for USA
  • ISBN 978-1-4614-4080-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $149.00
price for USA
  • ISBN 978-1-4899-9175-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Ramanujan's Lost Notebook
Book Subtitle
Part IV
Authors
Copyright
2013
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
Distribution Rights
Distribution rights for India: Delhi Book Store, New Delhi, India
eBook ISBN
978-1-4614-4081-9
DOI
10.1007/978-1-4614-4081-9
Hardcover ISBN
978-1-4614-4080-2
Softcover ISBN
978-1-4899-9175-1
Edition Number
1
Number of Pages
XVII, 439
Topics