On the Zeroes of Half-Integral Weight Eisenstein Series on ${\Gamma }_0(4)$

Samantha C. Moore

We locate all but $O(\sqrt{k\log k})$ zeroes of the half integral weight Eisenstein series $E_{\infty }(z,k)$ of ${\Gamma }_0(4)$ for $k$ sufficiently large. To do this, we relate $E_\infty(…