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In this paper we give a simple proof of an inequality for intermediate Diophantine exponents obtained recently by W.M. Schmidt and L. Summerer. 相似文献
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N. G. Moshchevitin 《Journal of Mathematical Sciences》2012,180(5):610-625
This paper is concerned with the existence of badly approximable numbers in problems involving lacunary or sublacunary sequences.
The principal results depend upon Peres–Schlag’s method. 相似文献
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N. G. Moshchevitin 《Mathematical Notes》1991,49(5):498-501
Translated from Matematicheskie Zametki, Vol. 49, No. 5, pp. 80–85, May, 1991. 相似文献
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Nikolay Moshchevitin 《Czechoslovak Mathematical Journal》2012,62(1):127-137
Let Θ = (θ
1,θ
2,θ
3) ∈ ℝ3. Suppose that 1, θ
1, θ
2, θ
3 are linearly independent over ℤ. For Diophantine exponents
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$\begin{gathered}
\alpha (\Theta ) = sup\left\{ {\gamma > 0: \mathop {\lim }\limits_{t \to } \mathop {\sup }\limits_{ + \infty } t^\gamma \psi _\Theta (t) < + \infty } \right\}, \hfill \\
\beta (\Theta ) = sup\left\{ {\gamma > 0: \mathop {\lim }\limits_{t \to } \mathop {\inf }\limits_{ + \infty } t^\gamma \psi _\Theta (t) < + \infty } \right\} \hfill \\
\end{gathered}$\begin{gathered}
\alpha (\Theta ) = sup\left\{ {\gamma > 0: \mathop {\lim }\limits_{t \to } \mathop {\sup }\limits_{ + \infty } t^\gamma \psi _\Theta (t) < + \infty } \right\}, \hfill \\
\beta (\Theta ) = sup\left\{ {\gamma > 0: \mathop {\lim }\limits_{t \to } \mathop {\inf }\limits_{ + \infty } t^\gamma \psi _\Theta (t) < + \infty } \right\} \hfill \\
\end{gathered} 相似文献
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N. G. Moshchevitin 《Mathematical Notes》1998,63(5):648-657
We prove that the integral of a smooth multifrequency conditionally periodic function with zero mean oscillates.
Translated fromMatematicheskie Zametki, Vol. 63, No. 5, pp. 737–748, May, 1998.
The author wishes to express his deep gratitude to S. V. Konyagin for fruitful discussions, verification of the results, and
the correction of some misprints.
This research was supported by the Russian Foundation for Basic Research under grants No. 96-01-00378 and No. 96-15-96072
and by the EFAKOD Foundation. 相似文献
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N. G. Moshchevitin 《Mathematical Notes》1997,61(5):590-599
For any monotone functionψ(y)=O(y
1/s), we prove the existence of a continual family of vectors (α1...,αs) admitting infinitely many simultaneous ψ-approximations, but nocψ-approximations with some constantc>0.
Translated fromMatematicheskie Zametki, Vol. 61, No. 5, pp. 706–716, May, 1997.
Translated by S. K. Lando 相似文献
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N. G. Moshchevitin 《Mathematical Notes》1995,58(5):1187-1196
We prove V. V. Kozlov's famous conjecture claiming that the integral of an analytic three-frequency conditionally periodic
function with zero mean and incommensurable frequencies recurs. For a conditionally periodic function of classC
2 onT
n
,n=2, 3, we prove that the integral recurs uniformly with respect to the initial data.
Translated fromMatematicheskie Zametki, Vol. 58, No. 5, pp. 723–735, November, 1995. 相似文献
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