Number theoretic considerations related to the scaling spectrum of self-similar measures with consecutive digits?

作者：Chi, Zi-Chao; Li, Qian; Lv, Jun^*

来源：Chaos, Solitons and Fractals, 2023, 173: 113648.

DOI：10.1016/j.chaos.2023.113648

• Self-similar measure
• Primitive
• Spectral eigenvalue problems
• Consecutive digits

Let 2 be two integers, and let D = , ... , . It is well known that the self-similar measure ,D generated by the iterated function system {????????????(??????) = (????????????)-1(??????+ ??????)}??????& ISIN;D is a spectral measure with a spectrum (& iota;finite l}JJJ n-ary sumation ??????(????????????, C) = (????????????)??????????????????& COLRATIO; ????????????& ISIN; C = {0, 1, ... , ??????- 1} . ??????=0 In this paper, we study a class of primitive and composite numbers and their related properties. And we also explore the simple prime numbers and the properties related to their order. Based on these, let ??????be a positive integer, we give some conditions on the distinct prime numbers ??????1, ??????2, ... , ????????????such that the scaling set jj ????????????=1 ?????????????????? ????????????(????????????, C) is also a spectrum of ??????????????????,K> 0.