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Ramanujan's Lost Notebook

Part III

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

  • Third 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 the ordinary partition function p(n), including ranks, cranks, and congruences for p(n)
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  • ISBN 978-1-4614-3810-6
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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 third of five volumes that the authors plan to write on Ramanujan’s lost notebook and other manuscripts and fragments found in The Lost Notebook and Other Unpublished Papers, published by Narosa in 1988.  The ordinary partition function p(n) is the focus of this third volume. In particular, ranks, cranks, and congruences for p(n) are in the spotlight. Other topics include the Ramanujan tau-function, the Rogers–Ramanujan functions, highly composite numbers, and sums of powers of theta functions.

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 a

nd 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 (10 chapters)

  • Introduction

    Andrews, George E. (et al.)

    Pages 1-7

  • Ranks and Cranks, Part I

    Andrews, George E. (et al.)

    Pages 9-44

  • Ranks and Cranks, Part II

    Andrews, George E. (et al.)

    Pages 45-70

  • Ranks and Cranks, Part III

    Andrews, George E. (et al.)

    Pages 71-88

  • Ramanujan’s Unpublished Manuscript on the Partition and Tau Functions

    Andrews, George E. (et al.)

    Pages 89-180

Buy this book

eBook $109.00
price for USA (gross)
  • ISBN 978-1-4614-3810-6
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $149.00
price for USA
  • ISBN 978-1-4614-3809-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $149.00
price for USA
  • ISBN 978-1-4899-9497-4
  • 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 III
Authors
Copyright
2012
Publisher
Springer-Verlag New York
Copyright Holder
The Editor(s) (if applicable) and The Author(s) 2018
eBook ISBN
978-1-4614-3810-6
DOI
10.1007/978-1-4614-3810-6
Hardcover ISBN
978-1-4614-3809-0
Softcover ISBN
978-1-4899-9497-4
Edition Number
1
Number of Pages
XII, 436
Topics