On the linear independence measures of logarithms of rational numbers. II

Abderraouf Bouchelaghem; Yuxin He; Yuanhang Li; Qiang Wu

doi:10.4134/JKMS.j230133

Journal of the
Korean Mathematical Society JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2024; 61(2): 293-307

Online first article February 16, 2024 Printed March 1, 2024

https://doi.org/10.4134/JKMS.j230133

On the linear independence measures of logarithms of rational numbers. II

Abderraouf Bouchelaghem, Yuxin He, Yuanhang Li, Qiang Wu

Tiansheng Road Beibei; Tiansheng Road Beibei; Tiansheng Road Beibei; Tiansheng Road Beibei

Abstract

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Abstract

In this paper, we give a general method to compute the linear independence measure of $1, \log(1-1/r),\log(1+1/s)$ for infinitely many integers $r$ and $s$. We also give improvements for the special cases when $r=s$, for example, $\nu(1, \log 3/4, \log 5/4) \leq 9.197$.

Keywords: Irrationality measure, linear independence measure, saddle point method

MSC numbers: 11J82, 11J86

Supported by: This work was supported by the Natural Science Foundation of China (Grant no. 12071375).