Abstract
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′ = Π p|q p of the modulus q satisfies log q′ ∼ log q. Some applications to zero free regions of Dirichlet L-functions and the Polya and Vinogradov inequalities are indicated.
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