On the central derivatives of l-functions and modularity of heenger cycles
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866908891313340416 |
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| author | Du, Tuoping Peng, Zhifeng |
| author_facet | Du, Tuoping Peng, Zhifeng |
| contents | This paper establishes an arithmetic intersection formula for central L-derivatives in higher weights.We prove that for a general cusp form (extending the previous result for newforms), the derivative is represented by the global height pairing between higher Heegner cycles. This result provides a framework for the Gross-Zagier-Zhang formula and its generalizations.Furthermore, we investigate the modularity of the generating series of Heegner cycles,proving a weak version of the conjecture and reducing the full modularity to a vanishing conjecture,for which we provide supporting evidence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_15795 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the central derivatives of l-functions and modularity of heenger cycles Du, Tuoping Peng, Zhifeng Number Theory 11G15, 11G18, 11F37 G.1.10 This paper establishes an arithmetic intersection formula for central L-derivatives in higher weights.We prove that for a general cusp form (extending the previous result for newforms), the derivative is represented by the global height pairing between higher Heegner cycles. This result provides a framework for the Gross-Zagier-Zhang formula and its generalizations.Furthermore, we investigate the modularity of the generating series of Heegner cycles,proving a weak version of the conjecture and reducing the full modularity to a vanishing conjecture,for which we provide supporting evidence. |
| title | On the central derivatives of l-functions and modularity of heenger cycles |
| topic | Number Theory 11G15, 11G18, 11F37 G.1.10 |
| url | https://arxiv.org/abs/2603.15795 |