A1 Refereed original research article in a scientific journal
Multilinear exponential sums with a general class of weights
Authors: Kerr Bryce, Macourt Simon
Publisher: SCUOLA NORMALE SUPERIORE
Publication year: 2021
Journal: Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze
Journal name in source: ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA-CLASSE DI SCIENZE
Journal acronym: ANN SCUOLA NORM-SCI
Volume: 22
Issue: 3
First page : 1105
Last page: 1130
Number of pages: 26
ISSN: 0391-173X
DOI: https://doi.org/10.2422/2036-2145.201908_017
Self-archived copy’s web address: https://arxiv.org/abs/1901.00975
Abstract
In this paper we obtain some new estimates for multilinear exponential sums in prime fields with a more general class of weights than previously considered. Our techniques are based on some recent progress of Shkredov in Additive Combinatorics with roots in Rudnev's point plane incidence bound. We apply our estimates to obtain new results concerning exponential sums with sparse polynomials and Weyl sums over small generalized arithmetic progressions.
In this paper we obtain some new estimates for multilinear exponential sums in prime fields with a more general class of weights than previously considered. Our techniques are based on some recent progress of Shkredov in Additive Combinatorics with roots in Rudnev's point plane incidence bound. We apply our estimates to obtain new results concerning exponential sums with sparse polynomials and Weyl sums over small generalized arithmetic progressions.
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