ZEROS OF A QUASI-MODULAR FORM OF WEIGHT 2 FOR Gamma(+)(0) (N)

Abstract

Basraoui and Sebbar showed that the Eisenstein series E-2 has infinitely many SL2(Z)-inequivalent zeros in the upper half-plane H, yet none in the standard fundamental domain F. They also found infinitely many such regions containing a zero of E-2 and infinitely many regions which do not have any zeros of E-2. In this paper we study the zeros of the quasi-modular form E-2(z) + NE2(Nz) of weight 2 for Gamma(+)(0) (N).