Abstract
Let $\Gamma$ be a congruence subgroup such that $\Gamma_{1}(N)\subset\Gamma\subset\Gamma_{0}(N)$ for some positive integer $N$. For a positive integer $k$, let $M_{k,\mathbf{Z}}(\Gamma)$ be the set of modular forms of weight $k$ on $\Gamma$ with integral Fourier coefficients. Let $R_{k}(\Gamma)$ be the set of common zeros in the upper half plane $\mathbf{H}$ of all the modular forms of weight $k$ on $\Gamma$. In this note, we prove that the density of modular forms in $M_{k,\mathbf{Z}}(\Gamma)$ with an algebraic zero $z \notin R_{k}(\Gamma)$ is zero.
Citation
Dohoon Choi. Youngmin Lee. Subong Lim. Jaegwang Ryu. "Proportion of modular forms with transcendental zeros for general levels." Proc. Japan Acad. Ser. A Math. Sci. 99 (2) 19 - 22, February 2023. https://doi.org/10.3792/pjaa.99.004