Description 
1 online resource (xi, 435 pages) : portraits (some color) 
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Introduction  Ranks and Cranks, Part I  Ranks and Cranks, Part II  Ranks and Cranks, Part III  Ramanujan's Unpublished Manuscript on the Partition and Tau Functions  Theorems about the Partition Function on Pages 189 and 182  Congruences for Generalized Tau Functions on Page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 RogersRamanujan Functions  Circular Summation  Highly Composite Numbers 
Summary 
Annotation 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plan to write on Ramanujans lost notebook and other manuscripts and fragments found in The Lost Notebook and Other Unpublished Papers, published by Narosa in 1988.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 taufunction, the RogersRamanujan 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 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 
Analysis 
Mathematics 

Number theory 
Bibliography 
Includes bibliographical references (pages 413429) and index 
Notes 
Online resource; title from PDF title page (SpringerLink, viewed November 7, 2013) 
Subject 
Ramanujan Aiyangar, Srinivasa, 18871920.


Ramanujan Aiyangar, Srinivasa, 18871920 

Mathematicians  India  Biography


Number theory.


Functions.


functions (mathematics)


MATHEMATICS  Algebra  Intermediate.


Matemáticos  Biografías  India


Funciones (Matemáticas)


Números , Teoría de


Functions


Mathematicians


Number theory


India

Genre/Form 
Biographies


Biographies.


Biographies.

Form 
Electronic book

Author 
Berndt, Bruce C., 1939

ISBN 
9781461438106 

1461438101 

1461438098 

9781461438090 
