Zeros of Quasimodular Forms Defined by Iterated Sums

We study the zeros of the quasimodular forms $G_{\{2\}^n}$ defined by iterated sums. We first show that, for every $n>0$, $G_{\{2\}^n}$ has exactly $n$ simple zeros on each of the vertical half-lines $\Real(τ)=0$ and $\Real(τ)=1/2$, and that the zeros for consecutive values of $n$ satisfy an interla