Research-Normal numbers with given limit of multiple ergodic averages

Research

All

Normal numbers with given limit of multiple ergodic averages

Speaker: Lingmin Liao（Wuhan University）
Time: Mar 21, 2024, 14:30-15:30
Location: M1001, College of Science Building

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.