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arXiv · 2104.05129

A Complex Borel-Bernstein Theorem

Gerardo González Robert
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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.

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Gerardo González Robert. 2021-04-11. A Complex Borel-Bernstein Theorem. https://arxiv.org/abs/2104.05129

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