Geodesic
About the Vahlen theorem analog for three-dimensional lattices
Dalʹnevostočnyj matematičeskij žurnal, Tome 2 (2001) no. 2, pp. 69-73.

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In this paper for three-dimensional lattices we study the analog of well-known Vahlen theorem about real number approximation of neighboring convergents of a continued fraction 
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M. O. Avdeeva. About the Vahlen theorem analog for three-dimensional lattices. Dalʹnevostočnyj matematičeskij žurnal, Tome 2 (2001) no. 2, pp. 69-73. http://geodesic.mathdoc.fr/item/DVMG_2001_2_2_a5/

[1] B. A. Venkov, Elementarnaya teoriya chisel, ONTI, Moskva, 1937, 219 pp.

[2] J. M. S. Cassels, An introduction to diophantine approximation, Cambridge, 1957; Vvedenie v teoriyu diofantovykh priblizhenii, M., 1961, 213 pp.

[3] G. F. Voronoi, Ob odnom obobschenii algoritma nepreryvnykh drobei, Sobranie sochinenii, v. 1, Kiev, 1952, 197–391

[4] H. Minkowski, “Zur Theorie der Kettenbruche”, Gesammelete Abhandlunden, Leipzig, 1991, 278–292

[5] V. A. Bykovskii, O. A. Gorkusha, “Minimalnye bazisy trekhmernykh polnykh reshetok”, Matematich. sb., 192:2 (2001), 57–66 | MR | Zbl

[6] V. A. Bykovskii, “Teorema Valena dlya dvumernykh podkhodyaschikh drobei”, Mat. zametki, 66:1 (1999), 30–37 | MR | Zbl