A1 Vertaisarvioitu alkuperäisartikkeli tieteellisessä lehdessä
Multilinear exponential sums with a general class of weights
Tekijät: Kerr Bryce, Macourt Simon
Kustantaja: SCUOLA NORMALE SUPERIORE
Julkaisuvuosi: 2021
Lehti: Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze
Tietokannassa oleva lehden nimi: ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA-CLASSE DI SCIENZE
Lehden akronyymi: ANN SCUOLA NORM-SCI
Vuosikerta: 22
Numero: 3
Aloitussivu: 1105
Lopetussivu: 1130
Sivujen määrä: 26
ISSN: 0391-173X
DOI: https://doi.org/10.2422/2036-2145.201908_017
Rinnakkaistallenteen osoite: https://arxiv.org/abs/1901.00975
Tiivistelmä
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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