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Matematicheskie Zametki, 2008, Volume 83, Issue 6, Pages 912–922
DOI: https://doi.org/10.4213/mzm4840 (Mi mzm4840) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Diophantine Approximations of the Number $\pi$ by Numbers from the Field $\mathbb Q(\sqrt{3})$

E. B. Tomashevskaya

Bryansk State Technical University
Full-text PDF (469 kB) Citations (2)
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DOI: https://doi.org/10.4213/mzm4840
Abstract: We prove an estimate of the irrationality measure of any nonzero number of the form $r_1\pi+r_2\pi/\sqrt{3}$, $r_1,r_2\in\mathbb Q(\sqrt{3})$.
Keywords: Diophantine approximation, the number $\pi$, the field $\mathbb Q(\sqrt{3})$, irrationality measure of a number, Kummer's formula, hypergeometric function, saddle-point method.
Received: 23.05.2007
English version:
Mathematical Notes, 2008, Volume 83, Issue 6, Pages 833–842
DOI: https://doi.org/10.1134/S0001434608050283
Bibliographic databases:
UDC: 511.36
Language: Russian
Citation: E. B. Tomashevskaya, “Diophantine Approximations of the Number $\pi$ by Numbers from the Field $\mathbb Q(\sqrt{3})$”, Mat. Zametki, 83:6 (2008), 912–922; Math. Notes, 83:6 (2008), 833–842
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
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