TY - JOUR
T1 - Equidistribution in the complex plane and self-similar measures
AU - Li, Wenxia
AU - Wang, Zhiqiang
AU - Xu, Jiayi
AU - Zhao, Jiuzhou
N1 - Publisher Copyright:
© The Author(s), 2025. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh.
PY - 2025
Y1 - 2025
N2 - We establish the pointwise equidistribution of self-similar measures in the complex plane. Let, whose complex conjugate is not a divisor of β, and a finite subset. Let μ be a non-atomic self-similar measure with respect to the IFS. For, if α and β are relatively prime, then we show that the sequence is equidistributed modulo one for μ-almost everywhere. We also discuss normality of radix expansions in Gaussian integer base, and obtain pointwise normality. Our results generalize partially the classical results in the real line to the complex plane.
AB - We establish the pointwise equidistribution of self-similar measures in the complex plane. Let, whose complex conjugate is not a divisor of β, and a finite subset. Let μ be a non-atomic self-similar measure with respect to the IFS. For, if α and β are relatively prime, then we show that the sequence is equidistributed modulo one for μ-almost everywhere. We also discuss normality of radix expansions in Gaussian integer base, and obtain pointwise normality. Our results generalize partially the classical results in the real line to the complex plane.
KW - equidistributed modulo one
KW - normal number
KW - p-adic interpolation
KW - radix expansions
KW - self-similar measures
UR - https://www.scopus.com/pages/publications/105015453321
U2 - 10.1017/prm.2025.10067
DO - 10.1017/prm.2025.10067
M3 - 文章
AN - SCOPUS:105015453321
SN - 0308-2105
JO - Proceedings of the Royal Society of Edinburgh Section A: Mathematics
JF - Proceedings of the Royal Society of Edinburgh Section A: Mathematics
ER -