On the zeros of certain weakly holomorphic modular forms for ${\varGamma }_0^+(5)$ and ${\varGamma }_0^+(7)$

Seiji Kuga Acta Arithmetica 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.

Authors

  • Seiji KugaGraduate School of Mathematics
    Kyushu University
    Motooka 744, Nishi-ku
    Fukuoka 819-0395, Japan
    e-mail

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