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Izv. RAN. Ser. Mat., 2018, Volume 82, Issue 4, Pages 3–17 (Mi izv8633)  

This article is cited in 2 scientific papers (total in 2 papers)

Kloosterman sums with multiplicative coefficients

M. A. Korolev

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: We obtain several new bounds for sums of the form
$$ S_{q}(x;f)=\mathop{{\sum}'}_{n\le x}f(n)e_{q}(an^*+bn), $$
in which $q$ is a sufficiently large integer, $\sqrt{q} (\log{q})\ll x\le q$, $a$ and $b$ are integers with $(a,q)=1$, $e_{q}(v) = e^{2\pi iv/q}$, $f(n)$ is a multiplicative function satisfying certain conditions, $nn^*\equiv 1 \pmod{q}$, and the prime in the sum means that $(n,q)=1$. The results in this paper refine similar bounds obtained earlier by Gong and Jia.

Keywords: inverse residues, Kloosterman sums, multiplicative functions.

Funding Agency Grant Number
Russian Science Foundation 14-11-00433
The work was completed at the Steklov Mathematical Institute and supported by the Russian Science Foundation (grant no. 14-11-00433).


DOI: https://doi.org/10.4213/im8633

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English version:
Izvestiya: Mathematics, 2018, 82:4, 647–661

Bibliographic databases:

UDC: 511.321
MSC: 11L05
Received: 24.11.2016
Revised: 20.03.2017

Citation: M. A. Korolev, “Kloosterman sums with multiplicative coefficients”, Izv. RAN. Ser. Mat., 82:4 (2018), 3–17; Izv. Math., 82:4 (2018), 647–661

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. M. A. Korolev, “New estimate for a Kloosterman sum with primes for a composite modulus”, Sb. Math., 209:5 (2018), 652–659  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    2. M. Korolev, I. Shparlinski, “Sums of algebraic trace functions twisted by arithmetic functions”, Pac. J. Math., 304:2 (2020), 505–522  crossref  isi
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