On character sums over flat numbers

2009/12/06 by Xi, Ping, Yi, Yuan
#11A07 #11L05 #11L40 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.0912.1071

Abstract

Let q\geqslant2 be an integer, χ be any non-principal character mod q, and H=H(q)\leqslant q. In this paper the authors prove some estimates for character sums of the form W(χ,H;q)=∑_n∈\mathscrF(H)χ(n), where \mathscrF(H)=\n∈ℤ|(n,q)=1,1\leqslant n,n\leqslant q, |n-n|\leqslant H\, n is defined by nn≡1\pmod q.

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