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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.15268 |
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| _version_ | 1866917273460015104 |
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| author | Jääsaari, Jesse |
| author_facet | Jääsaari, Jesse |
| contents | We show that for $\gg K^2$ of the half-integral weight Hecke cusp forms in the 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_15268 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the Real Zeroes of Half-integral Weight Hecke Cusp Forms, II Jääsaari, Jesse Number Theory We show that for $\gg K^2$ of the half-integral weight Hecke cusp forms in the 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. |
| title | On the Real Zeroes of Half-integral Weight Hecke Cusp Forms, II |
| topic | Number Theory |
| url | https://arxiv.org/abs/2601.15268 |