On the zeros of certain weakly holomorphic modular forms for ${\varGamma }_0^+(5)$ and ${\varGamma }_0^+(7)$
Volume 201 / 2021
Acta Arithmetica 201 (2021), 219-239
MSC: 11F03, 11F11.
DOI: 10.4064/aa200318-3-4
Published online: 18 October 2021
Abstract
Let $p$ be a prime for which $\Gamma _0^+(p)$ is of genus zero, and let $M_k^!(\Gamma _0^+(p))$ be the space of weakly holomorphic modular forms of weight $k$ for $\Gamma _0^+(p) $. It is known that $M_k^!(\Gamma _0^+(p))$ has the natural basis. In this paper, we consider the cases of $p=5,7$ and prove that for almost all elements in the natural basis, all of their zeros in a fundamental domain lie on the boundary arcs.
