Estimates for character sums and Dirichlet $L$-functions to smooth moduli (1503.07156v1)

Published 24 Mar 2015 in math.NT

Abstract: We use the $q$-analogue of van der Corput's method to estimate short character sums to smooth moduli. If $\chi$ is a primitive Dirichlet character modulo a squarefree, $q^{\delta$-smooth} integer $q$ we show that $$L(\frac12,\chi)\ll_\epsilon q^{{\frac{27}{164}+O(\delta)+\epsilon}.$$}