CONTINUED FRACTIONS FOR A CLASS OF TRIANGLE GROUPS
2012 ◽
Vol 93
(1-2)
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pp. 21-42
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Keyword(s):
AbstractWe give continued fraction algorithms for each conjugacy class of triangle Fuchsian group of signature $(3, n, \infty )$, with $n\geq 4$. 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.
Keyword(s):
2012 ◽
Vol 88
(9)
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pp. 145-148
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Keyword(s):
2001 ◽
Vol 71
(239)
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pp. 1271-1280
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Keyword(s):
1978 ◽
Vol 19
(2)
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pp. 173-197
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Keyword(s):
2013 ◽
Vol 143
(5)
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pp. 893-903
Keyword(s):
1982 ◽
Vol 19
(6)
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pp. 1637-1652
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