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. © 2021, Sociedad Matemática Mexicana.

publication date

• 2022-01-01

published in

• Boletin de la Sociedad Matematica Mexicana  Journal

keywords

• Complex Diophantine approximation; Continued fractions; Metrical Diophantine approximation

Digital Object Identifier (DOI)

• 10.1007/s40590-021-00399-z

PubMed ID

start page

end page

volume

• 28

issue

• 1