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Remarks on the Pólya–Vinogradov Inequality

Carl Pomerance
Published Online: 2011-08-04 | DOI: https://doi.org/10.1515/integ.2011.039


We establish a numerically explicit version of the Pólya–Vinogradov inequality for the sum of values of a Dirichlet character on an interval. While the technique of proof is essentially that of Landau from 1918, the result we obtain has better constants than in other numerically explicit versions that have been found more recently.

Keywords.: Dirichlet Character; Gauss Sum; Pólya–Vinogradov Inequality

About the article

Received: 2010-01-25

Accepted: 2010-07-10

Published Online: 2011-08-04

Published in Print: 2011-08-01

Citation Information: Integers, Volume 11, Issue 4, Pages 531–542, ISSN (Print) 1867-0652, DOI: https://doi.org/10.1515/integ.2011.039.

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