Algebraic trace functions over the primes

We study sums over primes of trace functions of \ell -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...

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Bibliographic Details
Published in:Duke mathematical journal 2014-06, Vol.163 (9), p.1683-1736
Main Authors: Fouvry, Étienne, Kowalski, Emmanuel, Michel, Philippe
Format: Article
Language:English
Subjects:
11F11
11L05
11N
11N05
11N32
11N35
11T23
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Summary:We study sums over primes of trace functions of \ell -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.
ISSN:0012-7094
1547-7398
DOI:10.1215/00127094-2690587