Geodesic
The distribution of solutions of a~determinantal equation
Sbornik. Mathematics, Tome 206 (2015) no. 7, pp. 988-1019

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{SM_2015_206_7_a4,
     author = {A. V. Ustinov},
     title = {The distribution of solutions of a~determinantal equation},
     journal = {Sbornik. Mathematics},
     pages = {988--1019},
     publisher = {mathdoc},
     volume = {206},
     number = {7},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2015_206_7_a4/}
}
TY  - JOUR
AU  - A. V. Ustinov
TI  - The distribution of solutions of a~determinantal equation
JO  - Sbornik. Mathematics
PY  - 2015
SP  - 988
EP  - 1019
VL  - 206
IS  - 7
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_2015_206_7_a4/
LA  - en
ID  - SM_2015_206_7_a4
ER  - 
%0 Journal Article
%A A. V. Ustinov
%T The distribution of solutions of a~determinantal equation
%J Sbornik. Mathematics
%D 2015
%P 988-1019
%V 206
%N 7
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_2015_206_7_a4/
%G en
%F SM_2015_206_7_a4
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/