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Local dimension of univoque bases

孔德荣 研究员
Wednesday, April 10th, 2019, 10:00 AM  闵行数学楼401报告厅
摘要:Fix an alphabet A={0,1,…,M}. The univoque set U of bases q in (1,M+1) in which the number 1 has a unique expansion over the alphabet A has been well studied. It has Lebesgue measure zero but Hausdorff dimension one. In this talk we will describe how the set U is distributed over the interval (1,M+1) by determining the local dimension of U. As an application we give a complete answer to a question of [P. Allaart, Adv. Math., 308:575--598, 2017] about strongly univoque sets. This is a joint work with Pieter Allaart.

主持人: 李文侠 教授
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