Vol. 11, No. 2, 2022

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On irrationality measure functions for several real numbers

Viktoria Rudykh

Vol. 11 (2022), No. 2, 197–204
Abstract

For an n-tuple α = (α1,,αn) of pairwise independent numbers we consider permutations

σ(t) : {1,2,3,,n}{σ1,σ2,σ3,,σn}, ψασ 1(t) > ψασ 2(t) > ψασ 3(t) > > ψασn(t),

of irrationality measure functions ψα(t) = min 1qtqα. Let 𝔨(α) be the number of infinitely occurring different permutations {σ1,,σ𝔨(α)}. We prove that the length of an n-tuple α with 𝔨(α) = k is

n k(k + 1) 2

and this result is optimal.

Keywords
irrationality measure function
Mathematical Subject Classification
Primary: 11J13
Milestones
Received: 27 April 2022
Revised: 24 June 2022
Accepted: 8 July 2022
Published: 13 August 2022
Authors
Viktoria Rudykh
Moscow Institute of Physics and Technology
Dolgoprudny
Russia