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Continued fractions with low complexity: transcendence measures and quadratic approximation
AbstractWe 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 exponentw2and Koksma's exponentw*2.doi:10.1112/s0010437x11007524 fatcat:cfqk2eerajcbve26ic6m2jrury