Zeros of modular forms of half integral weight

2016/02/01 by Amanda Folsom, Folsom, Amanda, Paul Jenkins +1
Mathematics · #11F30 #11F37 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11F30 #msc:11F37

paper · pdf · doi:10.48550/arxiv.1602.00589

arxiv created 2016/02/02 · arxiv updated 2016/02/04

Abstract

We study canonical bases for spaces of weakly holomorphic modular forms of level 4 and weights in ℤ+(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 Γ₀(4) lie on a lower boundary arc of the fundamental domain. Additionally, we show that at many places on this arc, the generating function for Hurwitz class numbers is equal to a particular mock modular Poincaré series, and show that for positive weights, a particular set of Fourier coefficients of cusp forms in this canonical basis cannot simultaneously vanish.

Related

• Zeros of weakly holomorphic modular forms of level 4
• Zeros of weakly holomorphic modular forms of levels 2 and 3
• Divisibility properties of coefficients of modular functions in genus zero levels
• Weakly holomorphic modular forms in prime power levels of genus zero
• Rationality and p-adic properties of reduced forms of half-integral weight