Number Theory in the Spirit of Ramanujan
The purpose of this booklet is to provide an introduction to a small fraction of Ramanujan's work on theta functions and q-series and their connection to number theory. Among the main topics are q-series and theta-functions, congruences for τ and partition functions, sums of squares and triangular numbers, Eisenstein series, hypergeometric functions and their relation to theta functions, and Rogers-Ramanujan continued fractions. Each chapter ends with notes containing various historical and bibliographic comments. There is also a short account of Ramanujan’s life in the introduction. The book would be suitable for junior and senior undergraduates and recent graduates.