On a case of joint Dirichlet approximations
https://doi.org/10.22405/2226-8383-2025-26-4-447-453
Abstract
This paper studies best simultaneous approximations of the second kind for linearly dependent irrationalities. It is shown that, starting from a certain point, they are determined by the convergents of the first irrationality, of which all others are multiples.
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; junior researcher
Nikolai Mihailovich Dobrovol’skii
Tula State Lev Tolstoy Pedagogical University
Russian Federation
Russian Federation
doctor of physical and mathematical sciences, professor
References
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Review
For citations:
Dobrovol’skii M.N., Dobrovol’skii N.N., Dobrovol’skii N.M. On a case of joint Dirichlet approximations. Chebyshevskii Sbornik. 2025;26(4):447-453. (In Russ.) https://doi.org/10.22405/2226-8383-2025-26-4-447-453
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