# 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
##### Keywords:
diophantine approximation of ln 2