Zeros of weakly holomorphic modular forms of levels 2 and 3

Sharon Anne Garthwaite; Paul Jenkins

Zeros of weakly holomorphic modular forms of levels 2 and 3

Number Theory 2013-05-14 v2

Authors: Sharon Anne Garthwaite , Paul Jenkins

Abstract

Let $M_k^\sharp(N)$ be the space of weakly holomorphic modular forms for $\Gamma_0(N)$ 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.

Keywords

weakly holomorphic modular forms zeros fundamental domain boundary arc canonical basis

Cite

@article{arxiv.1205.7050,
  title  = {Zeros of weakly holomorphic modular forms of levels 2 and 3},
  author = {Sharon Anne Garthwaite and Paul Jenkins},
  journal= {arXiv preprint arXiv:1205.7050},
  year   = {2013}
}

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Added a reference, corrected typos

Zeros of weakly holomorphic modular forms of levels 2 and 3

Abstract

Keywords

Cite

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