Linking the Circle and the Sieve: Ramanujan - Fourier Series

Abstract

Currently the circle and the sieve methods are the key tools in analytic number theory. In this paper the unifying theme of the two methods is shown to be the Ramanujan - Fourier series.

18 pages, Based on a talk given at the Conference in Number Theory held at NIAS, Bangalore, India during 13-15, December 2003 in honor of Professor K. Ramachandra