Effective simultaneous rational approximation to pairs of real quadratic numbers (1907.10253v1)

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