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홈 > 학술정보 >학술행사 > 세미나
2017 POSTECH Math Colloquium

Title
The irrationality exponent of real numbers and the expansion in integer base
Speaker
Dong Han Kim   (Dongguk University )
Date
2017-10-20 15:50:00
Host
POSTECH
Place
Math. Bldg. 404
Abstract
We deduce a lower bound for the irrationality exponent of real numbers whose sequence of b-ary 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 b-ary expansion of xi cannot be 'too simple', in a suitable sense. Let r and s be multiplicatively independent positive integers. We establish that the r-ary expansion and the s-ary 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.
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