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Ramanujan's lost notebook: part III

By: Andrews,George E.
Contributor(s): Berndt, Bruce C [Co author].
Material type: materialTypeLabelBookPublisher: New York Springer 2012Description: xi, 435p. With index.ISBN: 9781493976263.Subject(s): Ramanujan Aiyangar, Srinivasa, 1887-1920 | Mathematics | Mathematics - algebraDDC classification: 510 Summary: 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plan to write on Ramanujan’s lost notebook and other manuscripts and fragments found in The Lost Notebook and Other Unpublished Papers, published by Narosa in 1988.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. https://www.springer.com/in/book/9781461438090
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Slot 1331 (0 Floor, East Wing) Non-fiction 510 A6R2 (Browse shelf) Available 198964

Table of contents
Introduction

Ranks and Cranks, Part I

Ranks and Cranks, Part II

Ranks and Cranks, Part III

Ramanujan’s Unpublished Manuscript on the Partition and Tau Functions

Theorems about the Partition Function on Pages 189 and 182

Congruences for Generalized Tau Functions on Page 178

Ramanujan’s Forty Identities for the Rogers–Ramanujan Functions

Circular Summation

Highly Composite Numbers

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.

https://www.springer.com/in/book/9781461438090

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