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arXiv · 0911.5547

Multiplicative mimicry and improvements of the Polya-Vinogradov inequality

Leo Goldmakher
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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. 2009-11-30. Multiplicative mimicry and improvements of the Polya-Vinogradov inequality. https://arxiv.org/abs/0911.5547

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