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Mat. Sb., 2019, Volume 210, Number 4, Pages 128–144 (Mi msb9006)  

On simultaneous approximations of $\ln3$ and $\pi/\sqrt3$ by rational numbers

A. A. Polyanskiiabcd

a Phystech School of Applied Mathematics and Informatics, Moscow Institute of Physics and Technology, Dolgoprudny, Moscow region, Russia
b Caucasus Mathematical Center, Adyghe State University, Maykop, Russia
c Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow, Russia
d Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia

Abstract: We prove an upper bound for the exponent of the simultaneous approximation of $\ln3$ and $\pi/\sqrt3$ by rational numbers.
Bibliography: 16 titles.

Keywords: irrationality measure, simultaneous approximations.

Funding Agency Grant Number
Russian Foundation for Basic Research 09-01-00743-а
This work was supported by the Russian Foundation for Basic Research (grant no. 09-01-00743-a).


DOI: https://doi.org/10.4213/sm9006

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English version:
Sbornik: Mathematics, 2019, 210:4, 589–605

Bibliographic databases:

UDC: 511.36
MSC: 11J82
Received: 25.08.2017 and 16.04.2018

Citation: A. A. Polyanskii, “On simultaneous approximations of $\ln3$ and $\pi/\sqrt3$ by rational numbers”, Mat. Sb., 210:4 (2019), 128–144; Sb. Math., 210:4 (2019), 589–605

Citation in format AMSBIB
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