On the Artin formalism for triple product $p$-adic $L$-functions: Chow--Heegner points vs. Heegner points
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914948666359808 |
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| author | Büyükboduk, Kâzım Casazza, Daniele Pal, Aprameyo de Vera-Piquero, Carlos |
| author_facet | Büyükboduk, Kâzım Casazza, Daniele Pal, Aprameyo de Vera-Piquero, Carlos |
| contents | Our main objective in this paper (which is expository for the most part) is to study the necessary steps to prove a factorization formula for a certain triple product $p$-adic $L$-function guided by the Artin formalism. The key ingredients are: a) the explicit reciprocity laws governing the relationship of diagonal cycles and generalized Heegner cycles to $p$-adic $L$-functions; b) a careful comparison of Chow--Heegner points and twisted Heegner points in Hida families, via formulae of Gross--Zagier type. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_08645 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Artin formalism for triple product $p$-adic $L$-functions: Chow--Heegner points vs. Heegner points Büyükboduk, Kâzım Casazza, Daniele Pal, Aprameyo de Vera-Piquero, Carlos Number Theory 11F66, 11F67, 11F33 (Primary) 11F85, 11G18, 14F30 (Secondary) Our main objective in this paper (which is expository for the most part) is to study the necessary steps to prove a factorization formula for a certain triple product $p$-adic $L$-function guided by the Artin formalism. The key ingredients are: a) the explicit reciprocity laws governing the relationship of diagonal cycles and generalized Heegner cycles to $p$-adic $L$-functions; b) a careful comparison of Chow--Heegner points and twisted Heegner points in Hida families, via formulae of Gross--Zagier type. |
| title | On the Artin formalism for triple product $p$-adic $L$-functions: Chow--Heegner points vs. Heegner points |
| topic | Number Theory 11F66, 11F67, 11F33 (Primary) 11F85, 11G18, 14F30 (Secondary) |
| url | https://arxiv.org/abs/2409.08645 |