On the common zeros of quasi-modular forms for Γ+0(N) of level N = 1, 2, 3

Abstract

In this article, we study common zeros of the iterated derivatives of the Eisenstein series for Γ0+(N){\Gamma }_{0}^{+}\left(N) of level N=1,2,and2,N=1,2, and 3, which are quasi-modular forms. More precisely, we investigate the common zeros of quasi-modular forms and prove that all the zeros of the iterated derivatives of the Eisenstein series θmEk(N){\theta }^{m}{E}_{k}^{\left(N)} of weight k=2,4,6k=2,4,6 for Γ0+(N){\Gamma }_{0}^{+}\left(N) of level N=2,3N=2,3 are simple by generalizing the results of Meher and Gun-Oesterlé for SL2(Z){{\rm{SL}}}_{2}\left({\mathbb{Z}}).

Keywords

• modular forms
• quasi-modular forms
• fricke group
• 11f11
• 11f99