Amanda Folsom

Affiliation: Amherst College

Email: afolsom@amherst.edu

Title Of Talk: Zeros of modular forms of half integral weight

Abstract: We study canonical bases for spaces of weakly holomorphic modular forms of level $4$ and weights in $\mathbb{Z} + \frac{1}{2}$, and show that almost all modular forms in these bases have the property that many of their zeros in a fundamental domain for $\Gamma_0(4)$ lie on a lower boundary arc. We also give applications to the mock modular generating function for Hurwitz class numbers, and to the simultaneous non-vanishing of associated cusp form coefficients. This is joint work with Paul Jenkins (Brigham Young University).

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