RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Izv. RAN. Ser. Mat.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


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

This article is cited in 1 scientific paper (total in 1 paper)

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

Full text: PDF file (662 kB)
First page: PDF file
References: PDF file   HTML file

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

Bibliographic databases:

Document Type: Article
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
\Bibitem{Kor18}
\by M.~A.~Korolev
\paper Kloosterman sums with multiplicative coefficients
\jour Izv. RAN. Ser. Mat.
\yr 2018
\vol 82
\issue 4
\pages 3--17
\mathnet{http://mi.mathnet.ru/izv8633}
\crossref{https://doi.org/10.4213/im8633}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2018IzMat..82..647K}
\elib{http://elibrary.ru/item.asp?id=35276427}
\transl
\jour Izv. Math.
\yr 2018
\vol 82
\issue 4
\pages 647--661
\crossref{https://doi.org/10.1070/IM8633}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000443002900001}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85053245348}


Linking options:
  • http://mi.mathnet.ru/eng/izv8633
  • https://doi.org/10.4213/im8633
  • http://mi.mathnet.ru/eng/izv/v82/i4/p3

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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  adsnasa  isi  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
    Number of views:
    This page:154
    References:9
    First page:10

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019