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arXiv · 1703.06965

Exponential sums over finite fields and the large sieve

Corentin Perret-Gentil
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Abstract

By using a variant of Kowalski's large sieve for Frobenius in compatible systems, we obtain zero-density estimates for arguments of $\ell$-adic trace functions over finite fields with values in some algebraic subsets of the cyclotomic integers, when the monodromy groups are known. This applies in particular to hyper-Kloosterman sums and general exponential sums considered by Katz.

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Corentin Perret-Gentil. 2019-10-22. Exponential sums over finite fields and the large sieve. https://doi.org/10.1093/imrn%2Frny202

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