The Serre Derivatives and Zeros of Modular Forms
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911670983458816 |
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| author | Sugibayashi, Naoki |
| author_facet | Sugibayashi, Naoki |
| contents | Since the work of F. Rankin and Swinnerton-Dyer on the zeros of Eisenstein series, many results have been obtained concerning the zeros of modular forms. In this paper, we study the zeros of Serre derivatives of modular forms. In particular, we prove that if all the zeros of a weakly holomorphic modular form in the standard fundamental domain lie on the lower boundary, then the same property holds for its Serre derivative. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_10227 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Serre Derivatives and Zeros of Modular Forms Sugibayashi, Naoki Number Theory 11F03, 11F11, 11F25 Since the work of F. Rankin and Swinnerton-Dyer on the zeros of Eisenstein series, many results have been obtained concerning the zeros of modular forms. In this paper, we study the zeros of Serre derivatives of modular forms. In particular, we prove that if all the zeros of a weakly holomorphic modular form in the standard fundamental domain lie on the lower boundary, then the same property holds for its Serre derivative. |
| title | The Serre Derivatives and Zeros of Modular Forms |
| topic | Number Theory 11F03, 11F11, 11F25 |
| url | https://arxiv.org/abs/2605.10227 |