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Conjugacy Classes and Binary Quadratic Forms for the Hecke Groups

Published online by Cambridge University Press:  20 November 2018

Giabao Hoang  and
Wendell Ressler
Giabao Hoang
Affiliation:
Department of Mathematics, Franklin & Marshall College, Lancaster, PA 17604 e-mail: giabao.hoang@fandm.eduwendell.ressler@fandm.edu
Wendell Ressler
Affiliation:
Department of Mathematics, Franklin & Marshall College, Lancaster, PA 17604 e-mail: giabao.hoang@fandm.eduwendell.ressler@fandm.edu
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Abstract.

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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 anyHecke group. We show that another consequence of our bound is that class numbers are finite for related hyperbolic $\mathbb{Z}\left[ \text{ }\!\!\lambda\!\!\text{ } \right]$-binary quadratic forms. We give canonical class representatives and calculate class numbers for some classes of hyperbolic $\mathbb{Z}\left[ \text{ }\!\!\lambda\!\!\text{ } \right]$-binary quadratic forms.

Keywords

11F0611E1611A55Hecke groupsconjugacy classquadratic forms
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 56 , Issue 3 , 01 September 2013 , pp. 570 - 583
Copyright
Copyright © Canadian Mathematical Society 2013

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