Zeros of certain weakly holomorphic modular forms for the Fricke group ${\varGamma }_0^+(3)$
Volume 197 / 2021
Acta Arithmetica 197 (2021), 37-54
MSC: Primary 11F03; Secondary 11F11.
DOI: 10.4064/aa190509-7-2
Published online: 11 September 2020
Abstract
Let $M_k^!(\Gamma _0^+(3))$ be the space of weakly holomorphic modular forms of weight $k$ for the Fricke group of level $3$. We introduce a natural basis for $M_k^!(\Gamma _0^+(3))$ and prove that for almost all basis elements, all of their zeros in a fundamental domain lie on the circle centered at 0 with radius ${1}/{\sqrt {3}}$.
