Continued fractions with low complexity: transcendence measures and quadratic approximation
Yann Bugeaud · Compositio Mathematica · 2012
Abstract We establish measures of non-quadraticity and transcendence measures for real numbers whose sequence of partial quotients has sublinear block complexity. The main new ingredient is an improvement of Liouville’s inequality giving a lower bound for the distance between two distinct quadratic real numbers. Furthermore, we discuss the gap between Mahler’s exponent w 2 and Koksma’s exponent w * 2 .