Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
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., 2008, Volume 72, Issue 1, Pages 39–50 (Mi izv1139)  

This article is cited in 4 scientific papers (total in 4 papers)

Waring's problem with the Ramanujan $\tau$-function

M. Z. Garaeva, V. C. Garciaa, S. V. Konyaginb

a National Autonomous University of Mexico, Institute of Mathematics
b M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: We prove that for every integer $N$ the Diophantine equation $\sum_{i=1}^{74000}\tau(n_i)=N$, where $\tau(n)$ is the Ramanujan $\tau$-function, has a solution in positive integers $n_1, n_2,…, n_{74000}$ satisfying the condition $\max_{1\le i\le 74000}n_i {\ll}|N|^{2/11}+1$. We also consider similar questions in residue fields modulo a large prime $p$.

DOI: https://doi.org/10.4213/im1139

Full text: PDF file (471 kB)
References: PDF file   HTML file

English version:
Izvestiya: Mathematics, 2008, 72:1, 35–46

Bibliographic databases:

UDC: 511.34
MSC: 11B83, 11B50, 11P32
Received: 12.07.2006

Citation: M. Z. Garaev, V. C. Garcia, S. V. Konyagin, “Waring's problem with the Ramanujan $\tau$-function”, Izv. RAN. Ser. Mat., 72:1 (2008), 39–50; Izv. Math., 72:1 (2008), 35–46

Citation in format AMSBIB
\Bibitem{GarGarKon08}
\by M.~Z.~Garaev, V.~C.~Garcia, S.~V.~Konyagin
\paper Waring's problem with the Ramanujan $\tau$-function
\jour Izv. RAN. Ser. Mat.
\yr 2008
\vol 72
\issue 1
\pages 39--50
\mathnet{http://mi.mathnet.ru/izv1139}
\crossref{https://doi.org/10.4213/im1139}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2394970}
\zmath{https://zbmath.org/?q=an:1180.11033}
\elib{https://elibrary.ru/item.asp?id=10336920}
\transl
\jour Izv. Math.
\yr 2008
\vol 72
\issue 1
\pages 35--46
\crossref{https://doi.org/10.1070/IM2008v072n01ABEH002390}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000254303700002}
\elib{https://elibrary.ru/item.asp?id=13571271}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-41549099126}


Linking options:
  • http://mi.mathnet.ru/eng/izv1139
  • https://doi.org/10.4213/im1139
  • http://mi.mathnet.ru/eng/izv/v72/i1/p39

    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. Garaev M.Z., Garcia V.C., Konyagin S.V., “The Waring problem with the Ramanujan $\tau$-function. II”, Canad. Math. Bull., 52:2 (2009), 195–199  crossref  mathscinet  zmath  isi  elib  scopus
    2. P. V. Snurnitsyn, “On the Basic Properties of the Ramanujan $\tau$-Function”, Math. Notes, 90:5 (2011), 723–729  mathnet  crossref  crossref  mathscinet  isi
    3. Snurnitsyn P.V., “O predstavimosti tselykh chisel znacheniyami funktsii Ramanudzhana”, Vestn. Mosk. un-ta. Ser. 1. Matem. Mekh., 2011, no. 6, 49–52  mathscinet  zmath  elib
    4. P. V. Snurnitsyn, “Additivnaya zadacha s funktsiei Ramanudzhana”, Chebyshevskii sb., 12:4 (2011), 112–128  mathnet  mathscinet
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
    Number of views:
    This page:743
    Full text:151
    References:44
    First page:20

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021