Mean values of character sums analogue of Kloosterman sums

Ping Xi

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arXiv · 1006.4256

Mean values of character sums analogue of Kloosterman sums

Ping Xi

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Abstract

Let $q$ be a positive integer, $\chi$ a nontrivial character mod $q$, $\mathcal{I}$ an interval of length not exceeding $q.$ In this paper we shall study the character sum analogue of the well-known Kloosterman sum,\[\sum_{\substack{a\in\mathcal{I} \gcd(a,q)=1}}\chi(ma+n\overline{a}),\] where $\overline{a}$ is the multiplicative inverse of $a\bmod q$. The mean square values and bilinear forms for such sums are proved.

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BibTeX RIS

Ping Xi. 2010-06-22. Mean values of character sums analogue of Kloosterman sums. https://arxiv.org/abs/1006.4256

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