Article
Approximations to Two Real Numbers
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Abstract
For a real ξ put ψ ξ(t) = min16x6t ||xξ||. Let α, β be real numbers such that α ± β 6∈ Z. We prove that the function ψα(t) − ψ β(t) changes its sign infinitely many often as t → +∞. The proof uses continued fractions.
Keywords
Continued fraction expansion, simultaneous approximation, badly approximate able number.
Citation
Kan, I. D. & Moshchevitin, N. G. (2010). Approximations to two real numbers. Uniform Distribution Theory, 5(2), 79–86.
I. D. Kan and N. G. Moshchevitin, “Approximations to two real numbers,” Uniform Distribution Theory, vol. 5, no. 2, pp. 79–86, 2010.
Kan ID, Moshchevitin NG. Approximations to two real numbers. Uniform Distribution Theory. 2010;5(2):79–86.
Kan, I. D. and Moshchevitin, N. G. (2010), ‘Approximations to two real numbers’, Uniform Distribution Theory, 5(2), pp. 79–86.
Kan, Igor D., and Nikolay G. Moshchevitin. “Approximations to Two Real Numbers.” Uniform Distribution Theory, vol. 5, no. 2, 2010, pp. 79–86.
Kan, Igor D., and Nikolay G. Moshchevitin. “Approximations to Two Real Numbers.” Uniform Distribution Theory 5, no. 2 (2010): 79–86.
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Published by: Engineering Journals
