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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.

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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}


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    Citing articles on Google Scholar: Russian citations, English citations
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    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
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