Mathematics

We study the location of zeros of the modular form $E_k^3 - E_{3k}$ of weight $3k$ in the standard fundamental domain $\mathcal{F}$ where $E_k$ is the Eisenstein series of weight$k$. We conjecture that all of its zeros are located on the bottom arc of $\mathcal{F}$ and on the line $x = \pm 1/2$.