AMS Chelsea Publishing 1991; 254 pp; hardcover Volume: 136 Reprint/Revision History: first AMS printing 1999; reprinted 2002 ISBN10: 0821820230 ISBN13: 9780821820230 List Price: US$39 Member Price: US$35.10 Order Code: CHEL/136.H
 Ramanujan occupies a unique place in analytic number theory. His formulas, identities, and calculations are still amazing threequarters of a century after his death. Many of his discoveries seem to have appeared as if from the ether. His mentor and primary collaborator was the famous G. H. Hardy. Here, Hardy collects twelve of his own lectures on topics stemming from Ramanujan's life and work. The topics include partitions, hypergeometric series, Ramanujan's \(\tau\)function and round numbers. Hardy was the first to recognize the brilliance of Ramanujan's ideas. As one of the great mathematicians of the time, it is fascinating to read Hardy's accounts of their importance and influence. The book concludes with a chapter by chapter overview written by Bruce C. Berndt. In this overview, Berndt gives references to current literature, developments since Hardy's original lectures, and background information on Ramanujan's research, including his unpublished papers. Readership Graduate students and research mathematicians interested in number theory. Reviews "From the fact that practically all topics of analytic number theory are mentioned, briefly or extensively, in this book in connection with one or the other of Ramanujan's ideas, theorems, conjectures, we realize the farreaching influence which his work has had on presentday mathematics ... the book is not only an homage to Ramanujan's genius; it is a survey of many branches of modern arithmetic and analysis and, altogether, a book which makes fascinating reading."  Hans Rademacher, Mathematical Reviews Table of Contents  The Indian mathematician Ramanujan
 Ramanujan and the theory of prime numbers
 Round numbers
 Some more problems of the analytic theory of numbers
 A latticepoint problem
 Ramanujan's work on partitions
 Hypergeometric series
 Asymptotic theory of partitions
 The representation of numbers as sums of squares
 Ramanujan's function \(\tau(n)\)
 Definite integrals
 Elliptic and modular functions
 Bibliography
