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Vahlen theorem for two-dimensional convergents

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Abstract

Certain properties of relative minima of three-dimensional lattices and simultaneous Diophantine approximations for two real numbers are studied.

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References

  1. G. F. Voronoy, “On a generalization of the algorithm of continued fractions,” in:Collected Works. Vol. 1 [in Russian], Kiev (1952), pp. 197–391.

  2. B. A. Venkov,Elementary Number Theory [in Russian], ONTI, Moscow (1937).

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  3. J. W. S. Cassels,An Introduction, to Diophantine Approximation, Cambridge Univ. Press, Cambridge (1957).

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Authors and Affiliations

  1. Khabarovsk Dept. of the Institute of Applied Math., Far Eastern Division, Russian Academy of Sciences, USSR

    V. A. Bykovskii

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  1. V. A. Bykovskii
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Translated fromMatematicheskie Zametki, Vol. 66, No. 1, pp. 30–37, July, 1999.

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Bykovskii, V.A. Vahlen theorem for two-dimensional convergents. Math Notes 66, 24–29 (1999). https://doi.org/10.1007/BF02674067

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  • DOI: https://doi.org/10.1007/BF02674067

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