Interlacing of zeros of weakly holomorphic modular forms

2013/08/05 by Paul Jenkins, Kyle Pratt, Jenkins, Paul +1
Mathematics · #11F03 #11F11 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11F03 #msc:11F11

paper · pdf · doi:10.48550/arxiv.1308.1123

arxiv created 2013/08/05 · arxiv updated 2013/08/07

Abstract

We prove that the zeros of a family of extremal modular forms interlace, settling a question of Nozaki. Additionally, we show that the zeros of almost all forms in a basis for the space of weakly holomorphic modular forms of weight k for \SL₂(ℤ) interlace on most of the lower boundary of the fundamental domain.

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