Bounds on short character sums and L-functions for characters with a smooth modulus

William Banks, Igor Shparlinski

Published 2016-05-24Version 1

We combine the classical idea of Postnikov (1956) with a method of Korobov (1974) for estimating double Weyl sums to derive new bounds on short character sums when the modulus $q$ has a small core $\mathfrak{q}_\sharp=\prod_{p\mid q}p$. Using this estimate, we improve certain bounds of Gallagher (1972) and Iwaniec (1974) for the corresponding $L$-functions.