Zeros of weakly holomorphic modular forms of level 4

2013/05/16 by Haddock, Andrew, Jenkins, Paul
#11F03 #11F11 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1305.3896

Abstract

Let M_k^\sharp(4) be the space of weakly holomorphic modular forms of weight k and level 4 that are holomorphic away from the cusp at ∞. We define a canonical basis for this space and show that for almost all of the basis elements, the majority of their zeros in a fundamental domain for Γ₀(4) lie on the lower boundary of the fundamental domain. Additionally, we show that the Fourier coefficients of the basis elements satisfy an interesting duality property.

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