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Search: MSC category 11F06 ( Structure of modular groups and generalizations; arithmetic groups [See also 20H05, 20H10, 22E40] )

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1. CMB 2012 (vol 56 pp. 570)

Hoang, Giabao; Ressler, Wendell
Conjugacy Classes and Binary Quadratic Forms for the Hecke Groups
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
Categories:11F06, 11E16, 11A55

2. CMB 2000 (vol 43 pp. 115)

Schmutz Schaller, Paul
Perfect Non-Extremal Riemann Surfaces
An infinite family of perfect, non-extremal Riemann surfaces is constructed, the first examples of this type of surfaces. The examples are based on normal subgroups of the modular group $\PSL(2,{\sf Z})$ of level $6$. They provide non-Euclidean analogues to the existence of perfect, non-extremal positive definite quadratic forms. The analogy uses the function {\it syst\/} which associates to every Riemann surface $M$ the length of a systole, which is a shortest closed geodesic of $M$.

Categories:11H99, 11F06, 30F45

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