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홈 > 학술정보 >학술행사 > 세미나
2017 고려대학교 수학과 학술강연

Title
The irrationality exponent of real numbers and the expansion in integer bases
Speaker
김동한   (동국대학교 )
Date
2017-10-13 04:30:00
Host
고려대학교
Place
아산이학관 524호
Abstract
We deduce a lower bound for the irrationality exponent of real numbers whose sequence of b-ary 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 b-aryexpansion of xi cannot be'toosimple',in a suitable sense. Letr 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 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.
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