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JOURNALS // Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika // Archive

Izv. Vyssh. Uchebn. Zaved. Mat., 2019 Number 1, Pages 69–75 (Mi ivm9431)

This article is cited in 5 papers

On irrationality measure $\mathrm{arctg}\, \frac {1}{3}$

V. Kh. Salikhov, M. G. Bashmakova

Bryansk State Technical University, 7 50-letiya Oktyabrya blvd., Bryansk, 241035 Russia

Abstract: We investigate the arithmetic properties of the value $\mathrm{arctg}\, \frac {1}{3}$. We elaborate special integral construction with the property of symmetry for evaluating irrationality measure of this number. We research linear form, generated by this integral, and prove a new result for extent of the irrationality of $\mathrm{arctg}\, \frac {1}{3}$, which improves the previous one.

Keywords: irrationality measure, linear form.

UDC: 511.36

Received: 20.11.2017
Revised: 20.11.2017
Accepted: 22.03.2018

DOI: 10.26907/0021-3446-2019-1-69-75


 English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2019, 63:1, 61–66

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© Steklov Math. Inst. of RAS, 2025