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Conjugacy Classes and Binary Quadratic Forms for the Hecke Groups |
14 pages
Published:2012-11-13
- Giabao Hoang,
- Wendell Ressler,
Abstract
In this paper we give a lower bound
with respect to block length
for the trace of non-elliptic conjugacy classes
of the Hecke groups.
One consequence of our bound
is that there are finitely many
conjugacy classes of a given trace in any Hecke group.
We show that another consequence of our bound
is that
class numbers are finite for
related hyperbolic \( \mathbb{Z}[\lambda] \)-binary quadratic forms.
We give canonical class representatives
and calculate class numbers
for some classes of hyperbolic \( \mathbb{Z}[\lambda] \)-binary quadratic forms.
| Keywords: | Hecke groups, conjugacy class, quadratic forms |
| MSC Classifications: |
11F06 - Structure of modular groups and generalizations; arithmetic groups [See also 20H05, 20H10, 22E40] 11E16 - General binary quadratic forms 11A55 - Continued fractions {For approximation results, see 11J70} [See also 11K50, 30B70, 40A15] |