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.
Citation
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