A family of weakly holomorphic modular forms for $\Gamma _0(2)$ with all zeros on a certain geodesic
Volume 190 / 2019
Acta Arithmetica 190 (2019), 57-74
MSC: Primary 11F03, 11F11.
DOI: 10.4064/aa171017-15-8
Published online: 14 June 2019
Abstract
We prove that certain infinitely many weakly holomorphic modular forms for $\Gamma_0(2)$ have all zeros on a part of a certain geodesic but not on the boundary of the fundamental domain $\mathfrak{F}$ of $\Gamma_0 (2)$, and prove that the zeros of one of these forms interlace with the zeros of another form.
