# Colloquium

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

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작성일Date

2017-10-16 10:44

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400

분야Field | 2017 Math Colloquium | ||
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날짜Date | 2017-10-20 | 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 baseAbstract: 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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