Ramanujan occupies a unique place in analytic number theory. His formulas, identities, and calculations are still amazing three-quarters 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developments since Hardy's original lectures, and background information on Ramanujan's research, including his unpublished papers.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 far-reaching influence which his work has had on present-day 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 lattice-point 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