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Минимальные системы векторов в трехмерных решетках и аналог теоремы Валена для трехмерных цепных дробей Минковского
Современные проблемы математики. 2012. № 16. С. 103–128.
Ustinov A.
The article is devoted to the development of the theory of three-dimensional continued fractions.
German O., Математический сборник 2026 Т. 217 № 2 С. 20–33
The spectrum of values of the weak uniform Diophantine exponents of lattices is studied, and its complete description in the two-dimensional case is given. ...
Added: February 20, 2026
Karpenkov O., Ustinov A., Journal of Number Theory 2017 Vol. 176 P. 375–419
In this paper we investigate the combinatorial structure of 3-dimensional Minkowski–Voronoi continued fractions. Our main goal is to prove the asymptotic stability of Minkowski–Voronoi complexes in special two-parametric families of rank-1 lattices. In addition we construct explicitly the complexes for the case of White's rank-1 lattices and provide with a hypothetic description in a more ...
Added: October 12, 2025
Вавилов В. В., Ustinov A., Квант 2006 № 6 С. 10–14
The article is devoted to problems related to possible arrangements of circles on plane lattices. ...
Added: October 12, 2025
Вавилов В. В., Ustinov A., Математическое образование 2006 № 4 С. 47–67
We continue publishing educational materials from the Specialized Educational and Scientific Center of Moscow State University (formerly Physics and Mathematics School No. 18). We offer three chapters from the brochure "Problems on Gridded Paper" by Specialized Educational and Scientific Center instructors V. V. Vavilov and A. V. Ustinov. The rest of the manual will be ...
Added: October 12, 2025
Вавилов В. В., Ustinov A., Математическое образование 2007 № 2 С. 33–57
We are completing the publication of the textbook "Problems on Gridded Paper" by V. V. Vavilov and A. V. Ustinov, instructors at the Moscow State University Specialized Educational and Scientific Center. The beginning of the textbook was published in issue 4(39), 2006. Similar issues are discussed in the book "Polygons on Lattice" by the same ...
Added: October 12, 2025
Вавилов В. В., Ustinov A., Квант 2007 № 6 С. 13–15
The article is devoted to semiregular polygons on lattices. ...
Added: October 12, 2025
Ustinov A., Дальневосточный математический журнал 2011 Т. 11 № 2 С. 213–221
Voronoi's algorithm for computing a system of fundamental units of a complex number field is based on a geometric properties of 3-dimensional lattices. This algorithm is based on Voronoi's theorem about cylindric minima for a lattice in general position. In the original proof and it's refinement published by Delone and Faddeev some significant cases were ...
Added: October 9, 2025
Ustinov A., Математические заметки 2014 Т. 95 № 1 С. 154–156
The article proposes a new proof of a three-dimensional analogue of Vahlen's theorem. ...
Added: October 9, 2025
Ustinov A., Математический сборник 2015 Т. 206 № 7 С. 103–134
In 1964, Linnik and Skubenko established the equidistribution of the integral points on the determinantal surface detX=P, where X is a (3×3) 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 (2×2) matrix). In this paper a more precise version of the Linnik-Skubenko reduction is proposed. It ...
Added: October 9, 2025
Ustinov A., Успехи математических наук 2015 Т. 70 № 3 С. 107–180
This survey is devoted to results related to metric properties of classical continued fractions and Voronoi–Minkowski three-dimensional continued fractions. The main focus is on applications of analytic methods based on estimates of Kloosterman sums. An apparatus is developed for solving problems about three-dimensional lattices. The approach is based on reduction to the preceding dimension, an ...
Added: October 9, 2025
Oleg N. German, Communications in Mathematics 2023 Vol. 31 No. 2 P. 27–33
In this paper we prove that uniform Diophantine exponents of lattices attain only trivial values. ...
Added: February 14, 2024
Rybakin A. S., Кулонен Г. А., СПб.: ВКАС им. Буденного, 1999.
Added: February 10, 2013