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This article is available for purchase or by subscription. See below.
Joint approximations of some values of the functions $\log x, \arctan x$

Mariya Bashmakova and Vladislav Salikhov
Vol. 13 (2024), No. 3, 225–238
DOI: 10.2140/cnt.2024.13.225
Abstract

Problems related to arithmetic properties of linear forms in various irrational and transcendental numbers, lower bounds for these linear forms, and approximation by rational fractions with bounded denominators are very popular in transcendence theory. We consider a new symmetric integral construction and prove a series of new lower bounds for joint approximations of certain values of the functions ln ⁡ x,arctan ⁡ x. Namely, the integral construction of such a type allows us to obtain new bounds for the linear forms |p + q ⋅ ln ⁡ W + r ⋅ arctan ⁡ V | with special values of W, V.

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Keywords
joint approximations, logarithmic function, arctangent function, linear form
Mathematical Subject Classification
Primary: 11J13
Milestones
Received: 1 April 2024
Revised: 30 June 2024
Accepted: 16 July 2024
Published: 16 August 2024
Authors
Mariya Bashmakova
Department of Higher Mathematics
Bryansk State Technical University
Bryansk
Russia
Vladislav Salikhov
Department of Higher Mathematics
Bryansk State Technical University
Bryansk
Russia
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