Zeros of weakly holomorphic modular forms of levels 2 and 3

2012/05/31 by Sharon Anne Garthwaite, Garthwaite, Sharon Anne, Paul Jenkins +1
Mathematics · #11F03 #11F11 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11F03 #msc:11F11

paper · pdf · doi:10.48550/arxiv.1205.7050

Added a reference, corrected typos

arxiv created 2013/05/13 · arxiv updated 2013/05/14

Abstract

Let M_k^\sharp(N) be the space of weakly holomorphic modular forms for Γ₀(N) that are holomorphic at all cusps except possibly at ∞. 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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