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2017 고려대학교 수학과 학술강연 



The irrationality exponent of real numbers and the expansion in integer bases 

We deduce a lower bound for the irrationality exponent of real numbers whose sequence of bary digitsis a Sturmian sequence over {0,1,…,b−1} and we prove that this lower bound is best possible. If their rationality exponent of xi is equal to 2 or slightly greater than 2, then the baryexpansion of xi cannot be'toosimple',in a suitable sense. Letr and s be multiplicatively independent positive integers. We establish that the rary expansion and the sary expansion of an irrational real number,viewed as infinite word son{0,1,...,r−1} and {0,1,...,s−1},respectively, cannot have simultaneously a low block complexity.In particular, they cannot be both Sturmian words.This talk is based on joint work with Yann Bugeaud. 







