Metric and arithmetic properties of mediant-Rosen maps

Mathematics – Number Theory

Scientific paper

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27 pages, 7 figures

Scientific paper

A continued fractions based verification of the Hurwitz values for the Hecke
triangle groups is given, completing a program of Lehner's. Ergodic theory
shows that Diophantine approximation by mediant convergents of the Rosen
continued fractions is sufficient to determine the values that Haas and Series
found by hyperbolic geometry.

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