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arXiv · 1309.1124

Kloosterman sums in residue rings

J. Bourgain·M. Z. Garaev
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Abstract

In the present paper, we generalize some of the results on Kloosterman sums proven in \cite{BG} for prime moduli to general moduli. This requires to establish the corresponding additive properties of the reciprocal set $$ I^{-1}=\{x^{-1}:\quad x\in I\}, $$ where $I$ is an interval in the ring of residue classes modulo a large positive integer. We apply our bounds on multilinear exponential sums to the Brun-Titchmarsh theorem and the estimate of very short Kloosterman sums, hence generalizing our earlier work to the setting of general modulus.

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J. Bourgain, M. Z. Garaev. 2013-09-04. Kloosterman sums in residue rings. https://arxiv.org/abs/1309.1124

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