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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
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
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
Linking options:
https://www.mathnet.ru/eng/mzm4840https://doi.org/10.4213/mzm4840 https://www.mathnet.ru/eng/mzm/v83/i6/p912
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Abstract page: | 507 | Full-text PDF : | 204 | References: | 79 | First page: | 4 |
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