Colloquium
The irrationality exponent of real numbers and the expansion in integer base
작성자Author
관리자
작성일Date
20171016 10:44
조회Views
474
분야Field  2017 Math Colloquium  

날짜Date  20171020  시간Time  15:50 ~ 18:00 
장소Place  Math. Bldg. 404  초청자Host  손영환 
연사Speaker  Dong Han Kim  소속Affiliation  Dongguk University 
TOPIC  The irrationality exponent of real numbers and the expansion in integer base  
소개 및 안내사항Content  Title: The irrationality exponent of real numbers and the expansion in integer base Abstract: 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. 
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