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2012 Multiplicative mimicry and improvements to the Pólya–Vinogradov inequality
Leo Goldmakher
Algebra Number Theory 6(1): 123-163 (2012). DOI: 10.2140/ant.2012.6.123

Abstract

We study exponential sums whose coefficients are completely multiplicative and belong to the complex unit disc. Our main result shows that such a sum has substantial cancellation unless the coefficient function is essentially a Dirichlet character. As an application we improve current bounds on odd-order character sums. Furthermore, conditionally on the generalized Riemann hypothesis we obtain a bound for odd-order character sums which is best possible.

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Leo Goldmakher. "Multiplicative mimicry and improvements to the Pólya–Vinogradov inequality." Algebra Number Theory 6 (1) 123 - 163, 2012. https://doi.org/10.2140/ant.2012.6.123

Information

Received: 21 October 2010; Accepted: 29 December 2010; Published: 2012
First available in Project Euclid: 20 December 2017

zbMATH: 1263.11076
MathSciNet: MR2950162
Digital Object Identifier: 10.2140/ant.2012.6.123

Subjects:
Primary: 11L40
Secondary: 11L03, 11L07

Rights: Copyright © 2012 Mathematical Sciences Publishers

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Vol.6 • No. 1 • 2012
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