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THE RESONANCE METHOD FOR LARGE CHARACTER SUMS

Part of: Multiplicative number theory Exponential sums and character sums

Published online by Cambridge University Press:  11 September 2012

Bob Hough
Bob Hough*
Affiliation:
Department of Mathematics, Stanford University, 450 Serra Mall, Stanford, CA 95070, U.S.A. (email: rdhough@math.stanford.edu)
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Abstract

We consider the size of large character sums, proving new lower bounds for Δ(N,q)=sup χ≠χ0 mod q∣∑ n<Nχ(n)∣ in almost all ranges of N. The proofs use the resonance method and saddle point analysis.

MSC classification

Secondary: 11L40: Estimates on character sums 11N25: Distribution of integers with specified multiplicative constraints 11N37: Asymptotic results on arithmetic functions
Type
Research Article
Information
Mathematika , Volume 59 , Issue 1 , January 2013 , pp. 87 - 118
Copyright
Copyright © University College London 2012

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