A generalization of the Pólya-Vinogradov inequality.

In this paper we consider an approach of Dobrowolski and Williams which leads to a generalization of the Pólya-Vinogradov inequality. We show how the Dobrowolski-Williams approach is related to the classical proof of Pólya-Vinogradov using Fourier analysis. Our results improve upon the earlier work of Bachman and Rachakonda (Ramanujan J. 5:65-71, ). In passing, we also obtain sharper explicit versions of the Pólya-Vinogradov inequality. [ABSTRACT FROM AUTHOR]