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Estimates for character sums and Dirichlet $L$-functions to smooth moduli
Published 24 Mar 2015 in math.NT | (1503.07156v1)
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 $$L(\frac12,\chi)\ll_\epsilon q{\frac{27}{164}+O(\delta)+\epsilon}.$$
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