Equidistribution for measures defined by digit restrictions

作者：Xiong, Ying^*; Zhao, Jiuzhou

来源：Nonlinearity, 2022, 35(8): 4064-4084.

DOI：10.1088/1361-6544/ac7693

• uniform distribution modulo one
• digit restrictions
• diversity of b-adic expansion

In this paper, we study the pointwise equidistribution properties of measures mu(p) defined by digit restrictions on the b-adic expansion, where b >= 2 is an integer. We prove that, if a sequence (alpha(n))(n >= 1) b-adic diversity condition, then the sequence (alpha(n)x)(n >= 1) mu(p)-a.e. x. We also find some sufficient conditions to ensure the b-adic diversity. Moreover, we apply these results to establish the b-adic diversity for the sequences that can be written as certain combination of polynomial and exponential functions.

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