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Mat. Sb., 2015, Volume 206, Number 7, Pages 103–134 (Mi msb8387)  

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

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).


DOI: https://doi.org/10.4213/sm8387

Full text: PDF file (679 kB)
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English version:
Sbornik: Mathematics, 2015, 206:7, 988–1019

Bibliographic databases:

Document Type: Article
UDC: 511.336+514.174.6
MSC: Primary 55R80; Secondary 11N45
Received: 20.05.2014 and 27.01.2015

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

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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. A. V. Ustinov, “Three-dimensional continued fractions and Kloosterman sums”, Russian Math. Surveys, 70:3 (2015), 483–556  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
  • Математический сборник Sbornik: Mathematics (from 1967)
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