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. Akad. Nauk SSSR Ser. Mat., 1985, Volume 49, Issue 2, Pages 393–426 (Mi izv1360)  

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

An asymptotic formula for the number of representations by totally positive ternary quadratic forms

Yu. G. Teterin


Abstract: Suppose $\mathfrak o$ is a maximal order of a totally real algebraic number field $K$; $f(x_1,x_2,x_3)$ is a totally positive quadratic form over $K$; $\mathfrak a$ and $\mathfrak c$ are ideals of the ring $\mathfrak o$; $m\in K$; and $x_1,x_2,x_3\in\mathfrak o$. The author proves an asymptotic formula for the number of solutions of the system
$$ f(x_1,x_2,x_3)=m,\quadg.c.d.(x_1,x_2,x_3)=\mathfrak c,\qquad x_1\equiv b_1, x_2\equiv b_2, x_3\equiv b_3\pmod{\mathfrak a} $$
in numbers $x_1,x_2,x_3\in\mathfrak o$. The proof is based on a discrete ergodic method.
Bibliography: 19 titles.

Full text: PDF file (3220 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Izvestiya, 1986, 26:2, 371–403

Bibliographic databases:

UDC: 511.512
MSC: 11E10, 11E20
Received: 09.06.1983

Citation: Yu. G. Teterin, “An asymptotic formula for the number of representations by totally positive ternary quadratic forms”, Izv. Akad. Nauk SSSR Ser. Mat., 49:2 (1985), 393–426; Math. USSR-Izv., 26:2 (1986), 371–403

Citation in format AMSBIB
\Bibitem{Tet85}
\by Yu.~G.~Teterin
\paper An~asymptotic formula for the number of representations by totally positive ternary quadratic forms
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1985
\vol 49
\issue 2
\pages 393--426
\mathnet{http://mi.mathnet.ru/izv1360}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=791309}
\zmath{https://zbmath.org/?q=an:0585.10011}
\transl
\jour Math. USSR-Izv.
\yr 1986
\vol 26
\issue 2
\pages 371--403
\crossref{https://doi.org/10.1070/IM1986v026n02ABEH001152}


Linking options:
  • http://mi.mathnet.ru/eng/izv1360
  • http://mi.mathnet.ru/eng/izv/v49/i2/p393

    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. U. M. Pachev, “Representation of integers by isotropic ternary quadratic forms”, Izv. Math., 70:3 (2006), 587–604  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. U. M. Pachev, “Obzor issledovanii po diskretnomu ergodicheskomu metodu v teorii chisel”, Chebyshevskii sb., 11:1 (2010), 217–233  mathnet  mathscinet
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
    Number of views:
    This page:165
    Full text:64
    References:40
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020