Original article

Mathematische Annalen

, Volume 318, Issue 2, pp 255-275

First online:

Fuchsian groups, automorphic functions and Schwarzians

  • John McKayAffiliated withDepartment of Mathematics and CICMA, Concordia University, 1455 de Maisonneuve Blvd. West, Montreal, Quebec H3G 1M8, Canada (e-mail: mckay@cs.concordia.ca)
  • , Abdellah SebbarAffiliated withDepartment of Mathematics and Statistics, University of Ottawa, Ottawa, ON K1N 6N5, Canada (e-mail: sebbar@mathstat.uottawa.ca)

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Abstract.

In this paper, a close connection is established between the geometry of certain genus zero Fuchsian groups and the analytic properties of the automorphic forms obtained by applying a certain differential operator to the Hauptmoduls of the groups.