Rational Period Functions for Γ0+(2) and Γ0+ (3)

Abstract

Knopp explored various properties of rational period functions for group SL2(Z) in relation to modular integrals on SL2(Z). In their study of Hecke-Weil correspondence, Hawkins and Knopp defined two types of modular integrals on a group Gamma 0+(p). When p is an element of{2, 3}, Choi and Kim introduced specific rational period functions for Gamma 0+(p)and established connections with one of the modular integrals on Gamma 0+(p) to obtain some properties of the rational period functions for Gamma 0+(p) which generalize results given by Knopp. In this paper, we define new rational period functions for Gamma 0+(p) that are associated with the other modular integrals on Gamma 0 +(p). Additionally, we discover several properties of these new rational period functions for Gamma 0+ (p).