×

zbMATH — the first resource for mathematics

A lower bound for the approximation of \(\ln 2\) by rational numbers. (Russian) Zbl 0635.10025
Let \(u\in [0,1]\), and let \(\varepsilon\) be any positive number. It is proved that for any positive integers \(p,q>q_0(\varepsilon,u)\) we have
\[ | q \ln 2-p| > q^{-\gamma -\varepsilon}, \] where \(\gamma =\gamma(u)\) is a complicated function of \(u\). Presumably, the best choice is \(u=1/7\) which leads to \(\gamma =2.893\).

MSC:
11J04 Homogeneous approximation to one number
PDF BibTeX XML Cite