A generalization of the Pólya–Vinogradov inequality
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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, 2001). In passing, we also obtain sharper explicit versions of the Pólya–Vinogradov inequality.
KeywordsArithmetic functions Dirichlet character Pólya–Vinogradov inequality
Mathematics Subject Classification11A25 11L40
The First author is supported by the Dynasty Foundation, by the Russian Foundation for Basic Research (grants no. 11-01-00759-a and no. 12-01-31165). The second author is partially supported by NSF grant DMS-1001068.
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