This article is cited in 3 papers

New Estimate for Kloosterman Sums with Primes

M. A. Korolev^a, M. E. Changa<sup>b

a</sup> Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
^b Moscow State University of Geodesy and Cartography

Abstract: We obtain an estimate for a Kloosterman sum with primes for an arbitrary modulus $q$ whose length $X$ satisfies the conditions
$$ q^{1/2+\varepsilon}\le X\ll q^{3/2}. $$
This estimate refines the results obtained earlier by E. Fouvry, I. E. Shparlinski (2011), and the first author (2018, 2019).

Keywords: Kloosterman sums, prime numbers, inverse residues.

UDC: 511.33

Received: 12.02.2020

DOI: 10.4213/mzm12693

 English version: Mathematical Notes, 2020, 108:1, 87–93

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