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Sbornik: Mathematics, 2015, Volume 206, Issue 7, Pages 988–1019
DOI: https://doi.org/10.1070/SM2015v206n07ABEH004486 (Mi sm8387) 		 
This article is cited in 1 scientific paper (total in 1 paper)

The distribution of solutions of a determinantal equation

A. V. Ustinov

Institute for Applied Mathematics, Khabarovsk Division, Far-Eastern Branch of the Russian Academy of Sciences, Dzerzhinsky st., 54, Khabarovsk, 680000, Russia
English version PDF (628 kB) Citations (1)
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DOI: https://doi.org/10.1070/SM2015v206n07ABEH004486
Abstract: 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.
Funding agency Grant number
Dynasty Foundation
Russian Foundation for Basic Research 14-01-90002
The research was supported by the "Dynasty" Foundation and the Russian Foundation for Basic Research (grant no. 14-01-90002).
Received: 20.05.2014 and 27.01.2015
Russian version:
Matematicheskii Sbornik, 2015, Volume 206, Number 7, Pages 103–134
DOI: https://doi.org/10.4213/sm8387
Bibliographic databases:
Document Type: Article
UDC: 511.336+514.174.6
MSC: Primary 55R80; Secondary 11N45
Language: English
Original paper language: Russian
Citation: A. V. Ustinov, “The distribution of solutions of a determinantal equation”, Mat. Sb., 206:7 (2015), 103–134; Sb. Math., 206:7 (2015), 988–1019
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
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