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Continued factions for a class of triangle groups

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https://ir.library.oregonstate.edu/concern/articles/mk61rn32j

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Abstract
  • We give continued fraction algorithms for each conjugacy class of triangle Fuchsian group of signature (3, n, ∞), with n ≥ 4. In particular, we give an explicit form of the group that is a subgroup of the Hilbert modular group of its trace field and provide an interval map that is piecewise linear fractional, given in terms of group elements. Using natural extensions, we find an ergodic invariant measure for the interval map. We also study Diophantine properties of approximation in terms of the continued fractions and show that these continued fractions are appropriate to obtain transcendence results.
  • This is the publisher’s final pdf. The published article is published by Cambridge University Press and copyrighted by Australian Mathematical Publishing Association Inc. and can be found at: http://www.cambridge.org/.
  • Keywords: Continued fractions, Diophantine approximation, Fuchsian groups
  • Keywords: Continued fractions, Diophantine approximation, Fuchsian groups
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  • Calta, K., & Schmidt, T. (2012). Continued fractions for a class of triangle groups. Journal of the Australian Mathematical Society, 93(1-2), 21-42. doi:10.1017/S1446788712000651
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Journal Volume
  • 93
Journal Issue/Number
  • 43467
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Urheberrechts-Erklärung
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