Exponential sums over finite fields and the large sieve

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.

29 pages; published version

References in corpus (2)

• Gaussian distribution of short sums of trace functions over finite fields
• Integral monodromy groups of Kloosterman sheaves

Cited by in corpus (1)

• Roots of $L$-functions of characters over function fields, generic linear independence and biases