Geodesic
The distribution of solutions of a determinantal equation
Sbornik. Mathematics, Tome 206 (2015) no. 7, pp. 988-1019 Cet article a éte moissonné depuis la source Math-Net.Ru

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In 1964, Linnik and Skubenko established the equidistribution of the integral points on the determinantal surface $\det X=P$, where $X$ is a $(3\times 3)$ matrix with independent entries and $P$ is an increasing parameter. Their method involved reducing the problem by one dimension (that is, to the determinantal equations with a $(2\times 2)$ matrix). In this paper a more precise version of the Linnik-Skubenko reduction is proposed. It can be applied to a wider range of problems arising in the geometry of numbers and in the theory of three-dimensional Voronoi-Minkowski continued fractions. Bibliography: 24 titles.
Keywords: lattices, Kloosterman sums. 
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A. V. Ustinov. The distribution of solutions of a determinantal equation. Sbornik. Mathematics, Tome 206 (2015) no. 7, pp. 988-1019. http://geodesic.mathdoc.fr/item/SM_2015_206_7_a4/

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