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Conformal Geometry and Dynamics

Published by the American Mathematical Society, the Conformal Geometry and Dynamics (ECGD) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4173

The 2020 MCQ for Conformal Geometry and Dynamics is 0.5.

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Subgroups of some Fuchsian groups defined by two linear congruences
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by Omer Yayenie PDF
Conform. Geom. Dyn. 11 (2007), 271-287 Request permission


In this article we define a new family of subgroups of Fuchsian groups $\mathcal {H}(\sqrt {m})$, for a squarefree positive integer $m$, and calculate their index in $\mathcal {H}(\sqrt {m})$ and their parabolic class number. Moreover, we will show that the index of these subgroups is closely related to the solvability of a quadratic congruence $x^2\equiv m(\textrm {mod }n)$ and the number of inequivalent solutions of a quadratic congruence $x^2\equiv 1(\textrm {mod }n)$. Finally, we will show that the results obtained by Yilmaz and Keskin [Acta Math. Sin 25 (2005), 215–222] are immediate corollaries of one of the main theorems of this article.
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Additional Information
  • Omer Yayenie
  • Affiliation: Department of Mathematics and Statistics, Murray State University, Murray, Kentucky 42071
  • Email:
  • Received by editor(s): March 26, 2007
  • Published electronically: December 18, 2007
  • © Copyright 2007 American Mathematical Society
  • Journal: Conform. Geom. Dyn. 11 (2007), 271-287
  • MSC (2000): Primary 11F06, 19B37; Secondary 20H05, 20H10
  • DOI:
  • MathSciNet review: 2365641