Zeros of certain combinations of Eisenstein series of weight 2k, 3k, and k + l

Jetjaroen Klangwang

We locate the zeros of the modular forms $E_k^2(\tau )+E_{2k}(\tau ),E_k^3(\tau )+E_{3k}(\tau ),$ and $E_k(\tau )E_l(\tau )+E_{k+l}(\tau ),$ where $E_k(\tau )$ is the Eisenstein series for the full modular…