On congruence equations arising from suborbital graphs

Abstract

In this paper we deal with congruence equations arising from suborbital graphs of the normalizer of Γ0(m) inPSL(2,R) . We also propose a conjecture concerning the suborbital graphs of the normalizer and the related congruenceequations. In order to prove the existence of solution of an equation over prime finite field, this paper utilizes theFuchsian group action on the upper half plane and Farey graphs properties.