On joint Dirichlet approximations of rationally dependent irrationalities
https://doi.org/10.22405/2226-8383-2026-27-2-171-179
Abstract
This paper studies best simultaneous approximations of the second kind for rationally dependent irrationalities. It is shown that, starting from a certain point, they are determined by the convergents of the common measure of these irrationalities, which are multiples of these irrationalities.
About the Authors
Mikhail Nikolaevich Dobrovol’skii
Geophysical centre of RAS
Russian Federation
Russian Federation
candidate of physical and mathematical sciences
Nikolai Nikolaevich Dobrovol’skii
Tula State Lev Tolstoy Pedagogical University; Lomonosov Moscow State University
Russian Federation
Russian Federation
doctor of physical and mathematical sciences, senior researcher
Nikolai Mihailovich Dobrovol’skii
Tula State Lev Tolstoy Pedagogical University
Russian Federation
Russian Federation
doctor of physical and mathematical sciences, professor
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Review
For citations:
Dobrovol’skii M.N., Dobrovol’skii N.N., Dobrovol’skii N.M. On joint Dirichlet approximations of rationally dependent irrationalities. Chebyshevskii Sbornik. 2026;27(2):171-179. (In Russ.) https://doi.org/10.22405/2226-8383-2026-27-2-171-179
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