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arXiv · 2601.15268

On the Real Zeroes of Half-integral Weight Hecke Cusp Forms, II

Jesse Jääsaari
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Abstract

We show that for $\gg K^2$ of the half-integral weight Hecke cusp forms in Kohnen plus subspaces with weight bounded by a large parameter $K$, the number of "real" zeroes grows at the expected rate. A key technical step in the proof is to obtain sharp bounds for the mollified first and second moments of quadratic twists of modular $L$-functions.

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Jesse Jääsaari. 2026-01-21. On the Real Zeroes of Half-integral Weight Hecke Cusp Forms, II. https://arxiv.org/abs/2601.15268

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