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arXiv · 2603.25071

Weak approximations, Diophantine exponents and two-dimensional lattices

Nikolay Moshchevitin
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Abstract

We study properties of Diophantine exponents of lattices and so-called related "weak" uniform approximations introduced in recent papers by Oleg German, in the simplest two-dimensional case. In contrast to the multidimensional case, in the two-dimensional case we can use a powerful tool of continued fractions. We develop an analog of Jarn\'{\i}k's theory dealing with inequalities between the ordinary and uniform Diophantine exponents, which turned out to be related to mutual behaviour of irrationality measure functions for two real numbers.

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Nikolay Moshchevitin. 2026-03-26. Weak approximations, Diophantine exponents and two-dimensional lattices. https://arxiv.org/abs/2603.25071

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