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On a problem related to “second” best approximations to a real number

Pavel Semenyuk

Vol. 12 (2023), No. 2, 175–180
Abstract

For a given irrational number α one can define an irrationality measure function related to the second-best approximations to α and consider the corresponding Diophantine constant and the corresponding spectrum consisting of these constants. In particular, two largest elements of the spectrum are already known. We calculate the value for the third element of the spectrum.

Keywords
Diophantine approximations
Mathematical Subject Classification
Primary: 11J06
Secondary: 11J70
Milestones
Received: 22 March 2023
Revised: 18 April 2023
Accepted: 2 May 2023
Published: 4 June 2023
Authors
Pavel Semenyuk
Moscow State University
Moscow
Russia