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JOURNALS // Trudy Matematicheskogo Instituta imeni V.A. Steklova // Archive

Trudy Mat. Inst. Steklova, 2017 Volume 296, Pages 163–180 (Mi tm3785)

This article is cited in 9 papers

Generalized Kloosterman sum with primes

M. A. Korolev

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: The work is devoted to generalized Kloosterman sums modulo a prime, i.e., trigonometric sums of the form $\sum _{p\le x}\exp \{2\pi i (a\overline {p}\,{+}\,F_k(p))/q\}$ and $\sum _{n\le x}\mu (n)\exp \{2\pi i (a\overline {n}\,{+}\,F_k(n))/q\}$, where $q$ is a prime number, $(a,q)=1$, $m\overline {m}\equiv 1\pmod q$, $F_k(u)$ is a polynomial of degree $k\ge 2$ with integer coefficients, and $p$ runs over prime numbers. An upper estimate with a power saving is obtained for the absolute values of such sums for $x\ge q^{1/2+\varepsilon }$.

UDC: 511.321

Received: April 13, 2016

DOI: 10.1134/S0371968517010137


 English version:
Proceedings of the Steklov Institute of Mathematics, 2017, 296, 154–171

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