V. A. Bykovskii, O. A. Gorkusha, “Minimal bases of three-dimensional complete lattices”, Sb. Math., 192:2 (2001), 215

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Sbornik: Mathematics, 2001, Volume 192, Issue 2, Pages 215–223
DOI: https://doi.org/10.1070/sm2001v192n02ABEH000542 (Mi sm542)

This article is cited in 8 scientific papers (total in 8 papers)

Minimal bases of three-dimensional complete lattices

V. A. Bykovskii, O. A. Gorkusha

Institute for Applied Mathematics, Khabarovsk Division, Far-Eastern Branch of the Russian Academy of Sciences

English version PDF (281 kB) Citations (8) Russian version article

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DOI: https://doi.org/10.1070/sm2001v192n02ABEH000542

Abstract: The Minkowski bases for three-dimensional lattices are studied.

Received: 24.06.1999

Bibliographic databases:

UDC: 511.36+511.9

MSC: Primary 11H06; Secondary 11J70

Language: English

Original paper language: Russian

Citation: V. A. Bykovskii, O. A. Gorkusha, “Minimal bases of three-dimensional complete lattices”, Sb. Math., 192:2 (2001), 215–223

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/sm542

https://doi.org/10.1070/sm2001v192n02ABEH000542

https://www.mathnet.ru/eng/sm/v192/i2/p57

This publication is cited in the following 8 articles:

A. V. Ustinov, “Three-dimensional continued fractions and Kloosterman sums”, Russian Math. Surveys, 70:3 (2015), 483–556
A. V. Ustinov, “On the Three-Dimensional Vahlen Theorem”, Math. Notes, 95:1 (2014), 136–138
Oleg Karpenkov, Algorithms and Computation in Mathematics, 26, Geometry of Continued Fractions, 2013, 357
A. V. Ustinov, “Minimal Vector Systems in 3-Dimensional Lattices and Analog of Vahlen's Theorem for 3-Dimensional Minkowski's Continued Fractions”, Proc. Steklov Inst. Math., 280, suppl. 2 (2013), S91–S116
A. A. Illarionov, “The average number of local minima of three-dimensional integer lattices”, St. Petersburg Math. J., 23:3 (2012), 551–570
M. O. Avdeeva, V. A. Bykovskii, “Refinement of Vahlen's Theorem for Minkowski Bases of Three-Dimensional Lattices”, Math. Notes, 79:2 (2006), 151–156
M. O. Avdeeva, V. A. Bykovskii, “An analogue of Vahlen's theorem for simultaneous approximations of a pair of numbers”, Sb. Math., 194:7 (2003), 955–967
M. O. Avdeeva, “Ob analoge teoremy Valena dlya trekhmernykh reshetok”, Dalnevost. matem. zhurn., 2:2 (2001), 69–73

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Statistics & downloads:
Abstract page:	564
Russian version PDF:	247
English version PDF:	18
References:	71
First page:	1

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