Generation of Hecke fields by squares of cyclotomic twists of modular $L$-values
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912639992463360 |
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| author | Blomer, Valentin Burungale, Ashay Michel, Philippe Min, Jun-Hwi |
| author_facet | Blomer, Valentin Burungale, Ashay Michel, Philippe Min, Jun-Hwi |
| contents | Let $f$ be a non-CM elliptic newform without a quadratic inner twist, $p$ an odd prime and $χ$ a Dirichlet character of $p$-power order and sufficiently large $p$-power conductor. We show that the compositum $\mathbb{Q}_{f}(χ)$ of the Hecke fields associated to $f$ and $χ$ is generated by the square of the absolute value of the corresponding central $L$-value $L^{\rm alg}(1/2, f \otimes χ)$ over $\mathbb{Q}(μ_p)$. The proof is based among other things on techniques used for the recent resolution of unipotent mixing conjecture by the first and third named authors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_15040 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generation of Hecke fields by squares of cyclotomic twists of modular $L$-values Blomer, Valentin Burungale, Ashay Michel, Philippe Min, Jun-Hwi Number Theory Let $f$ be a non-CM elliptic newform without a quadratic inner twist, $p$ an odd prime and $χ$ a Dirichlet character of $p$-power order and sufficiently large $p$-power conductor. We show that the compositum $\mathbb{Q}_{f}(χ)$ of the Hecke fields associated to $f$ and $χ$ is generated by the square of the absolute value of the corresponding central $L$-value $L^{\rm alg}(1/2, f \otimes χ)$ over $\mathbb{Q}(μ_p)$. The proof is based among other things on techniques used for the recent resolution of unipotent mixing conjecture by the first and third named authors. |
| title | Generation of Hecke fields by squares of cyclotomic twists of modular $L$-values |
| topic | Number Theory |
| url | https://arxiv.org/abs/2503.15040 |