Duke Mathematical Journal

Algebraic trace functions over the primes

Étienne Fouvry, Emmanuel Kowalski, and Philippe Michel

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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.

Article information

Source
Duke Math. J., Volume 163, Number 9 (2014), 1683-1736.

Dates
First available in Project Euclid: 12 June 2014

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1402578556

Digital Object Identifier
doi:10.1215/00127094-2690587

Mathematical Reviews number (MathSciNet)
MR3217765

Zentralblatt MATH identifier
1318.11103

Subjects
Primary: 11N05: Distribution of primes
Secondary: 11N 11N32: Primes represented by polynomials; other multiplicative structure of polynomial values 11N35: Sieves 11F11: Holomorphic modular forms of integral weight 11T23: Exponential sums 11L05: Gauss and Kloosterman sums; generalizations

Citation

Fouvry, Étienne; Kowalski, Emmanuel; Michel, Philippe. Algebraic trace functions over the primes. Duke Math. J. 163 (2014), no. 9, 1683--1736. doi:10.1215/00127094-2690587. https://projecteuclid.org/euclid.dmj/1402578556


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