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Mathematics of the USSR-Izvestiya, 1986, Volume 26, Issue 2, Pages 371–403
DOI: https://doi.org/10.1070/IM1986v026n02ABEH001152
(Mi im1360)
 

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
References:
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
$$ f(x_1,x_2,x_3)=m,\quad\text{g.c.d.}(x_1,x_2,x_3)=\mathfrak c,\qquad x_1\equiv b_1,\ x_2\equiv b_2,\ x_3\equiv b_3\pmod{\mathfrak a} $$
in numbers $x_1,x_2,x_3\in\mathfrak o$. The proof is based on a discrete ergodic method.
Bibliography: 19 titles.
Received: 09.06.1983
Bibliographic databases:
UDC: 511.512
MSC: 11E10, 11E20
Language: English
Original paper language: Russian
Citation: Yu. G. Teterin, “An asymptotic formula for the number of representations by totally positive ternary quadratic forms”, 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 Math. USSR-Izv.
\yr 1986
\vol 26
\issue 2
\pages 371--403
\mathnet{http://mi.mathnet.ru//eng/im1360}
\crossref{https://doi.org/10.1070/IM1986v026n02ABEH001152}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=791309}
\zmath{https://zbmath.org/?q=an:0585.10011}
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  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
     
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