TRANSCENDENCE AND NORMALITY OF COMPLEX NUMBERS VIA HURWITZ CONTINUED FRACTIONS

作     者：García-Ramos, Felipe Robert, Gerardo González Hussain, Mumtaz 

作者机构：Physics Institute Universidad Autónoma de San luis Potosí Mexico Faculty of Mathematics and Computer Science Uniwersytet Jagielloński Poland Department of Mathematical and Physical Sciences La Trobe University Bendigo3552 Australia 

出 版 物：《arXiv》 (arXiv)

年 卷 期：2023年

核心收录：

主　　题：Topology 

摘      要：We study the topological, dynamical, and descriptive set-theoretic properties of Hurwitz continued fractions. Hurwitz continued fractions associate an infinite sequence of Gaussian integers to every complex number which is not a Gaussian rational. The resulting space of sequences of Gaussian integers Ω is not closed. Using an iterative procedure, we show that Ω contains a natural subset whose closure R encodes continued fraction expansions of complex numbers which are not Gaussian rationals. We prove that (R, σ) is a subshift with a feeble specification property. As an application, we determine the rank in the Borel hierarchy of the set of Hurwitz normal numbers with respect to the complex Gauss measure. We also construct a family of complex transcendental numbers with bounded partial *** Codes 11J70 (Primary) 03E15, 11J81 (Secondary) © 2023, CC BY.