Interlacing of zeros of weakly holomorphic modular forms

Paul Jenkins; Kyle Pratt

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arXiv · 1308.1123

Interlacing of zeros of weakly holomorphic modular forms

Paul Jenkins·Kyle Pratt

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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 $\SL_2(\mathbb{Z})$ interlace on most of the lower boundary of the fundamental domain.

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Paul Jenkins, Kyle Pratt. 2013-08-05. Interlacing of zeros of weakly holomorphic modular forms. https://arxiv.org/abs/1308.1123

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