Effective simultaneous rational approximation to pairs of real quadratic numbers

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 $$\max \{\Vert q\xi \Vert ,\Vert q\zeta \Vert \}>q^{-1+\tau },$$ where $\Vert \cdot \Vert$ denotes the distance to the nearest integer.

9 pages

References in corpus (1)

• On the digital representation of integers with bounded prime factors