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Normal numbers with given limit of multiple ergodic averages

演讲者：廖灵敏（武汉大学）
时间：2024-03-21 14:30-15:30
地点：理学院大楼M1001

Abstract

We prove that the Hausdorff dimension of the set of normal numbers in base 2 whose binary expansions have the property that for any k, the k-th digits and the 2k-th digits are not all equal to 1, is one-half. Further, we obtain the Hausdorff dimension formula for the set of normal numbers in base 2 with given limit of multiple ergodic averages of some special function. This is a joint work with Michal Rams.