Vol. 9, No. 4, 2020

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Approximating $\pi$ by numbers in the field $\mathbb{Q}(\sqrt{3})$

Mikhail Yu. Luchin and Vladislav Kh. Salikhov

Vol. 9 (2020), No. 4, 421–433
Abstract

Using a new integral construction which combines the idea of symmetry suggested by V. Salikhov in 2007 and the integral introduced by Marcovecchio in 2009, we obtain a new bound for approximation to π by numbers from the field (3).

Keywords
irrationality measure, linear form, complex integral
Mathematical Subject Classification 2010
Primary: 11J17
Milestones
Received: 15 December 2019
Revised: 9 September 2020
Accepted: 23 September 2020
Published: 5 November 2020
Authors
Mikhail Yu. Luchin
Department of Higher Mathematics
Bryansk State Technical University
Bryansk
Russia
Vladislav Kh. Salikhov
Department of Higher Mathematics
Bryansk State Technical University
Bryansk
Russia