Geodesic
A family of weakly holomorphic modular forms for $\Gamma _0(2)$ with all zeros on a certain geodesic
SoYoung Choi1 ; Bo-Hae Im2
1 Department of Mathematics Education and RINS Gyeongsang National University 501 Jinjudae-ro Jinju, 52828, South Korea
2 Department of Mathematical Sciences KAIST 291 Daehak-ro, Yuseong-gu Daejeon, 34141, South Korea
Acta Arithmetica, Tome 190 (2019) no. 1, pp. 57-74 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/aa171017-15-8
Keywords: prove certain infinitely many weakly holomorphic modular forms gamma have zeros part certain geodesic boundary fundamental domain mathfrak gamma prove zeros these forms interlace zeros another form

SoYoung Choi 1 ; Bo-Hae Im 2

1 Department of Mathematics Education and RINS Gyeongsang National University 501 Jinjudae-ro Jinju, 52828, South Korea
2 Department of Mathematical Sciences KAIST 291 Daehak-ro, Yuseong-gu Daejeon, 34141, South Korea 
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     title = {A family of weakly holomorphic modular forms for $\Gamma _0(2)$ with all zeros on a certain geodesic},
     journal = {Acta Arithmetica},
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SoYoung Choi; Bo-Hae Im. A family of weakly holomorphic modular forms for $\Gamma _0(2)$ with all zeros on a certain geodesic. Acta Arithmetica, Tome 190 (2019) no. 1, pp. 57-74. doi: 10.4064/aa171017-15-8

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