Abstract

For real $\xi$ we consider the irrationality measure function ${\psi }_{\xi }(t)=\underset{1\le q\le t,q\in \mathbb{Z}}{\min <!--FUNCTION\; APPLICATION-->}\parallel q\xi$$\parallel$. We prove that in the case $\alpha \pm \beta \notin \mathbb{Z}$ there exist arbitrary large values of $t$ with

The constant on the right-hand side is optimal.

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