On the best joint Dirichlet approximations
https://doi.org/10.22405/2226-8383-2025-26-4-432-437
Abstract
This paper develops a program for finding best joint approximations of the second kind for dependent irrationalities.
The results of calculations using the mathcad15 computer mathematics system are presented, confirming the conclusions of [2] that, starting from a certain point, all joint best approximations of the second kind for dependent random variables are determined by the denominators of the convergents of the fundamental irrationality, of which all others are multiples.
About the Authors
Irina Nikolaevna Balaba
Tula State Lev Tolstoy Pedagogical University
Russian Federation
Russian Federation
doctor of physical and mathematical sciences, professor
Ivan Nikolaevich Gavrilov
Tula State Lev Tolstoy Pedagogical University
Russian Federation
Russian Federation
student
Tatyana Alekseevna Kalinkina
Tula State Lev Tolstoy Pedagogical University
Russian Federation
Russian Federation
student
Natalya Vasilievna Medvedeva
Tula State Lev Tolstoy Pedagogical University
Russian Federation
Russian Federation
student
Veronika Sergeevna Solovieva
Tula State Lev Tolstoy Pedagogical University
Russian Federation
Russian Federation
student
Ekaterina Sergeevna Ulchenko
Tula State Lev Tolstoy Pedagogical University
Russian Federation
Russian Federation
student
References
1. G. Davenport, 1965, "Higher Arithmetic: An Introduction to Number Theory" / G. Davenport; translated from English by B. Z. Moroz; edited by Yu. V. Linnik. – Moscow: Nauka
2. M. N. Dobrovolsky, N. N. Dobrovolsky, N. M. Dobrovolsky, 2024, "On a case of joint Dirichlet approximations" , Chebyshevskii sbornik, vol. 26, no. 4, pp.
3. Feldman N. I. 1981, "Approximation of algebraic numbers." — Moscow: Izd-vo Mosk. University, p. 200
4. A. Ya. Khinchin, 1961, “Continued fractions”, Moscow: Fizmatlit.
Review
For citations:
Balaba I.N., Gavrilov I.N., Kalinkina T.A., Medvedeva N.V., Solovieva V.S., Ulchenko E.S. On the best joint Dirichlet approximations. Chebyshevskii Sbornik. 2025;26(4):432-437. (In Russ.) https://doi.org/10.22405/2226-8383-2025-26-4-432-437
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