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A Complex Borel-Bernstein Theorem
Gerardo González Robert
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…
Good's Theorem for Hurwitz Continued Fractions
Gerardo González Robert
Good's Theorem for regular continued fraction states that the set of real numbers such that has Hausdorff dimensi…
Purely Periodic and Transcendental Complex Continued Fractions
Gerardo Gonzalez Robert
Adolf Hurwitz proposed in 1887 a continued fraction algorithm for complex numbers: Hurwitz continued fractions (HCF). Among other similarities between HCF and regular continued fra…
Generalized Thue-Morse Continued Fractions
Gerardo González Robert
The Thue-Morse sequence is generalized to the sequences and two equivalent definitions are given. This generalization leads to transcendental numbers and has Queffélec's the…