On the Tamagawa number conjecture for modular forms twisted by anticyclotomic Hecke characters
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909820814098432 |
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| author | Sano, Takamichi |
| author_facet | Sano, Takamichi |
| contents | Let $f \in S_{2r}(Γ_0(N))$ be a normalized newform of weight $2r$ which is good at $p$. Let $K$ be an imaginary quadratic field of class number one in which every prime divisor of $pN$ splits. Let $χ$ be an anticyclotomic Hecke character of $K$ which is crystalline at the primes above $p$ and such that $L(f,χ,r)\neq 0$. We prove that the Tamagawa number conjecture for the critical value $L(f,χ,r)$ follows from the Iwasawa main conjecture for the Bertolini-Darmon-Prasanna $p$-adic $L$-function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_01601 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Tamagawa number conjecture for modular forms twisted by anticyclotomic Hecke characters Sano, Takamichi Number Theory Let $f \in S_{2r}(Γ_0(N))$ be a normalized newform of weight $2r$ which is good at $p$. Let $K$ be an imaginary quadratic field of class number one in which every prime divisor of $pN$ splits. Let $χ$ be an anticyclotomic Hecke character of $K$ which is crystalline at the primes above $p$ and such that $L(f,χ,r)\neq 0$. We prove that the Tamagawa number conjecture for the critical value $L(f,χ,r)$ follows from the Iwasawa main conjecture for the Bertolini-Darmon-Prasanna $p$-adic $L$-function. |
| title | On the Tamagawa number conjecture for modular forms twisted by anticyclotomic Hecke characters |
| topic | Number Theory |
| url | https://arxiv.org/abs/2510.01601 |