#### Vol. 9, No. 4, 2020

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Effective simultaneous rational approximation to pairs of real quadratic numbers

### Yann Bugeaud

Vol. 9 (2020), No. 4, 353–360
##### Abstract

Let $\xi$, $\zeta$ be quadratic real numbers in distinct quadratic fields. We establish the existence of effectively computable, positive real numbers $\tau$ and $c$ such that, for every integer $q$ with $q>c$, we have

$max\left\{\parallel q\xi \parallel ,\parallel q\zeta \parallel \right\}>{q}^{-1+\tau },$

where $\parallel \cdot \parallel$ denotes the distance to the nearest integer.

 To the memory of Naum Ilich Feldman (1918–1994)
##### Keywords
simultaneous approximation, Pell equation, linear form in logarithms
##### Mathematical Subject Classification 2010
Primary: 11J13
Secondary: 11D09, 11J86