A Complex Borel-Bernstein Theorem
Number Theory
2021-11-04 v3
Abstract
Zero-one laws are a central topic in metric Diophantine approximation. A classical example of such laws is the Borel-Bernstein theorem. In this note, we prove a complex analogue of the Borel-Bernstein theorem for complex Hurwitz continued fractions. As a corollary, we obtain a complex version of Khinchin's theorem on Diophantine approximation.
Keywords
Cite
@article{arxiv.2104.05129,
title = {A Complex Borel-Bernstein Theorem},
author = {Gerardo González Robert},
journal= {arXiv preprint arXiv:2104.05129},
year = {2021}
}
Comments
10 pages, 0 figures. I fixed some typos. The paper will appear on the Bolet\'in de la Sociedad Matem\'atica Mexicana. The published version may differ slighlty from this one