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arXiv · 0912.1071

On character sums over flat numbers

Ping Xi·Yuan Yi
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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 \[\mathcal{W}(χ,H;q)=\sum_{n\in\mathscr{F}(H)}χ(n),\] where \[\mathscr{F}(H)=\left\{n\in\mathbb{Z}|(n,q)=1,1\leqslant n,\bar{n}\leqslant q, |n-\bar{n}|\leqslant H\},\] $\bar{n}$ is defined by $n\bar{n}\equiv1\pmod q.$

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Ping Xi, Yuan Yi. 2009-12-06. On character sums over flat numbers. https://arxiv.org/abs/0912.1071

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