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15 June 2014 Algebraic trace functions over the primes
Étienne Fouvry, Emmanuel Kowalski, Philippe Michel
Duke Math. J. 163(9): 1683-1736 (15 June 2014). DOI: 10.1215/00127094-2690587

Abstract

We study sums over primes of trace functions of -adic sheaves. Using an extension of our earlier results on algebraic twists of modular forms to the case of Eisenstein series and bounds for Type II sums based on similar applications of the Riemann hypothesis over finite fields, we prove general estimates with power saving for such sums. We then derive various concrete applications.

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Étienne Fouvry. Emmanuel Kowalski. Philippe Michel. "Algebraic trace functions over the primes." Duke Math. J. 163 (9) 1683 - 1736, 15 June 2014. https://doi.org/10.1215/00127094-2690587

Information

Published: 15 June 2014
First available in Project Euclid: 12 June 2014

zbMATH: 1318.11103
MathSciNet: MR3217765
Digital Object Identifier: 10.1215/00127094-2690587

Subjects:
Primary: 11N05
Secondary: 11F11, 11L05, 11N, 11N32, 11N35, 11T23

Rights: Copyright © 2014 Duke University Press

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Vol.163 • No. 9 • 15 June 2014
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