Short character sums for composite moduli

Details Short character sums for composite moduli Short character sums for composite moduli

2011-12-31

arxiv.org/abs/1201.0299v1

Mathematics

Number Theory

Scientific paper

We establish new estimates on short character sums for arbitrary composite moduli with small prime factors. Our main result improves on the Graham-Ringrose bound for square free moduli and also on the result due to Gallagher and Iwaniec when the core $q'=\prod_{p|q}p$ of the modulus $q$ satisfies $\log q'\sim \log q$. Some applications to zero free regions of Dirichlet L-functions and the $\rm{P\acute{o}lya}$ and Vinogradov inequalities are indicated.

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