Über die Funktionen des Irrationalitätsmaßes für zwei irrationalen Zahlen

Abstract

For real $\xi$ we consider irrationality measure function ${\psi }_{\xi }(t)={\min }_{1\le q\le t,q\in \mathbb{Z}}||q\xi ||$. We prove that in the case $\alpha \pm \beta \notin \mathbb{Z}$ there exist arbitrary large values of $t$ with $|{\psi }_{\alpha }(t)-{\psi }_{\beta }(t)|\ge \left(\sqrt{\frac{\sqrt{5}+1}{2}}-1\right)\min ({\psi }_{\alpha }(t),{\psi }_{\beta }(t))$. This result is optimal.

6 pages, in German