This article is cited in 16 papers

Karatsuba's method for estimating Kloosterman sums

M. A. Korolev

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: Using Karatsuba's method, we obtain estimates for Kloosterman sums modulo a prime, in which the number of terms is less than an arbitrarily small fixed power of the modulus. These bounds refine similar results obtained earlier by Bourgain and Garaev.
Bibliography: 16 titles.

Keywords: short Kloosterman sums, Karatsuba's method, inverse residues.

UDC: 511.33

MSC: 11L05

Received: 09.12.2015 and 06.04.2016

DOI: 10.4213/sm8648

 English version: Sbornik: Mathematics, 2016, 207:8, 1142–1158

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