A Complex Borel-Bernstein Theorem
arXiv:2104.05129
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.
10 pages, 0 figures. I fixed some typos. The paper will appear on the Boletín de la Sociedad Matemática Mexicana. The published version may differ slighlty from this one