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A family of weakly holomorphic modular forms for $\Gamma _0(2)$ with all zeros on a certain geodesic

Volume 190 / 2019

SoYoung Choi, Bo-Hae Im 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.

Authors

  • SoYoung ChoiDepartment of Mathematics Education
    and RINS
    Gyeongsang National University
    501 Jinjudae-ro
    Jinju, 52828, South Korea
    e-mail
  • Bo-Hae ImDepartment of Mathematical Sciences
    KAIST
    291 Daehak-ro, Yuseong-gu
    Daejeon, 34141, South Korea
    e-mail

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