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The best two-dimensional simultaneous Diophantine approximations in sup-norm. (Russian, English) Zbl 1103.41029

Vestn. Mosk. Univ., Ser. I 2005, No. 6, 50-53 (2005); translation in Mosc. Univ. Math. Bull. 60, No. 6, 29-32 (2005).
For the exponent \(g_2\) of growth of the best two-dimensional diophantine approximations in sup-norm the estimate \(g_2>1,28^+\) is obtained. This is a refinement of the Lagarias result [see J. S. Lagarias, Trans. Am. Math. Soc. 272, No. 2, 545–554 (1982; Zbl 0495.10021)].

MSC:

41A50 Best approximation, Chebyshev systems
11D99 Diophantine equations

Citations:

Zbl 0495.10021
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