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developments since Hardy's original lectures, and background information on Ramanujan's research, including his unpublished papers.
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978-0-8218-2023-0 (9780821820230)
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Schweitzer Klassifikation
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.
