On the Zeros of the Miller Basis of Cusp Forms
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912696510709760 |
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| author | Raveh, Roei |
| author_facet | Raveh, Roei |
| contents | We study the zeros of cusp forms in the Miller basis whose vanishing order at infinity is a fixed number $m$. We show that for sufficiently large weights, the finite zeros of such forms in the fundamental domain, all lie on the circular part of the boundary of the fundamental domain. We further show and quantify an effective bound for the weight, which is linear in terms of $m$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_01184 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Zeros of the Miller Basis of Cusp Forms Raveh, Roei Number Theory We study the zeros of cusp forms in the Miller basis whose vanishing order at infinity is a fixed number $m$. We show that for sufficiently large weights, the finite zeros of such forms in the fundamental domain, all lie on the circular part of the boundary of the fundamental domain. We further show and quantify an effective bound for the weight, which is linear in terms of $m$. |
| title | On the Zeros of the Miller Basis of Cusp Forms |
| topic | Number Theory |
| url | https://arxiv.org/abs/2405.01184 |