Mathematical Research Letters

Volume 20 (2013)

Number 4

Zeros of weakly holomorphic modular forms of levels 2 and 3

Pages: 657 – 674

DOI: http://dx.doi.org/10.4310/MRL.2013.v20.n4.a5

Authors

Sharon Anne Garthwaite (Department of Mathematics, Bucknell University, Lewisburg, Pennsylvania, U.S.A.)

Paul Jenkins (Department of Mathematics, Brigham Young University, Provo, Utah, U.S.A.)

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.

2010 Mathematics Subject Classification

11F03, 11F11

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