RAMANUJAN

Abstract

PROF. G. H. HARDY who, some thirteen years ago, supervised the editing of Ramanujan's collected papers, has now produced a new volume dealing with Ramanujan.* It is a series of essays rather than a systematic account of his work. However, it includes most of his more important discoveries, and alss much recent work associated with the results found by Ramanujan. There are twelve essays, and it will make my subsequent remarks more intelligible if I give their titles in full: (1) The Indian mathematician Ramanujan; (2) Ramanujan and the theory of prime numbers; (3) Round numbers; (4) Some more problems of the analytic theory of numbers; (5) A lattice point problem; (6) Ramanujan's work on partitions; (7) Hypergeometric series; (8) Asymptotic theory of partitions; (9) The representation of numbers as sums of squares; (10) Ramanujan's function τ(n); (11) Definite integrals; (12) Elliptic and modular functions.