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Zeros of certain weakly holomorphic modular forms for the Fricke group ${\varGamma }_0^+(3)$

Volume 197 / 2021

Seiichi Hanamoto, Seiji Kuga 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 ${1}/{\sqrt {3}}$.

Authors

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

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