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2017 POSTECH Math Colloquium 



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

Dong Han Kim (Dongguk University ) 
We deduce a lower bound for the irrationality exponent of real numbers whose sequence of bary digits is a Sturmian sequence over {0,1,…,b−1} and we prove that this lower bound is best possible. If the irrationality exponent of xi is equal to 2 or slightly greater than 2, then the bary expansion of xi cannot be 'too simple', in a suitable sense. Let r 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 words on {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. 







