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Short character sums for composite moduli

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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 Pólya and Vinogradov inequalities are indicated.

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Authors and Affiliations

  1. Department of Mathematics, University of California, Riverside, CA, 92521, USA

    Mei-Chu Chang

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  1. Mei-Chu Chang
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Correspondence to Mei-Chu Chang.

Additional information

Research partially financed by the NSF Grant DMS 1301608. Part of the work was finished when the author was in residence at the Mathematical Science Research Institute and supported by the NSF Grant 0932078000.

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Chang, MC. Short character sums for composite moduli. JAMA 123, 1–33 (2014). https://doi.org/10.1007/s11854-014-0012-y

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  • DOI: https://doi.org/10.1007/s11854-014-0012-y

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