Determination of a pair of newforms from the product of their twisted central values
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929220285890560 |
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| author | Anamby, Pramath Pal, Ritwik |
| author_facet | Anamby, Pramath Pal, Ritwik |
| contents | We show that a pair of newforms $(f,g)$ can be uniquely determined by the product of the central $L$-values of their twists. To achieve our goal, we prove an asymptotic formula for the average of the product of the central values of two twisted $L$-functions- $L(1/2, f \times χ)L(1/2, g \times χψ)$, where $(f,g)$ is a pair of newforms. The average is taken over the primitive Dirichlet characters $χ$ and $ψ$ of distinct prime moduli. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_12891 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Determination of a pair of newforms from the product of their twisted central values Anamby, Pramath Pal, Ritwik Number Theory Primary 11F11, 11F66, 11F67 We show that a pair of newforms $(f,g)$ can be uniquely determined by the product of the central $L$-values of their twists. To achieve our goal, we prove an asymptotic formula for the average of the product of the central values of two twisted $L$-functions- $L(1/2, f \times χ)L(1/2, g \times χψ)$, where $(f,g)$ is a pair of newforms. The average is taken over the primitive Dirichlet characters $χ$ and $ψ$ of distinct prime moduli. |
| title | Determination of a pair of newforms from the product of their twisted central values |
| topic | Number Theory Primary 11F11, 11F66, 11F67 |
| url | https://arxiv.org/abs/2401.12891 |