The location of zeros of a quasi-modular form of weight 2 for Gamma(+)(0)(p) for p=2, 3

Abstract

Let E-2(z) be the Eisenstein series which is quasi-modular of weight 2 for SL2(Z). For each p = 2,3, we show that there are infinitely many Gamma(+)(0)(p)-inequivalent zeros of the quasi-modular form E(z) := E-2(z) + pE(2)(pz) of weight 2 for Gamma(+)(0)(p) and give the estimates of their locations numerically. (C) 2016 Elsevier Inc. All rights reserved.