This article is cited in 1 paper

New estimates for short Kloosterman sums with weights

N. K. Semenova

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: In the paper we obtain a new bound for short Kloosterman sums modulo a prime with a weight. The derivation of the bound is based on Karatsuba's method (1993–1995) of estimating incomplete Kloosterman sums and on a modification of the method proposed by Bourgain and Garaev (2014). The theorems proved in the paper refine results obtained earlier by Korolev (2010).

Keywords: short Kloosterman sums, reciprocals modulo a given integer.

UDC: 511.321

MSC: 11L05

Received: 19.03.2021
Revised: 12.05.2021

DOI: 10.4213/im9168

 English version: Izvestiya: Mathematics, 2022, 86:3, 560–585

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