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arXiv · 1205.7050

Zeros of weakly holomorphic modular forms of levels 2 and 3

Sharon Anne Garthwaite·Paul Jenkins
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Abstract

Let $M_k^\sharp(N)$ be the space of weakly holomorphic modular forms for $Γ_0(N)$ that are holomorphic at all cusps except possibly at $\infty$. We study a canonical basis for $M_k^\sharp(2)$ and $M_k^\sharp(3)$ and prove that almost all modular forms in this basis have the property that the majority of their zeros in a fundamental domain lie on a lower boundary arc of the fundamental domain.

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Sharon Anne Garthwaite, Paul Jenkins. 2013-05-13. Zeros of weakly holomorphic modular forms of levels 2 and 3. https://arxiv.org/abs/1205.7050

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