Toroidal families and averages of L-functions, I
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866907910684016640 |
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| author | Fouvry, Étienne Kowalski, Emmanuel Michel, Philippe |
| author_facet | Fouvry, Étienne Kowalski, Emmanuel Michel, Philippe |
| contents | We initiate the study of certain families of $L$-functions attached to characters of subgroups of higher-rank tori, and of their average at the central point. In particular, we evaluate the average of the values $L(\demi,χ^a)L(\demi,χ^b)$ for arbitrary integers~$a$ and~$b$ when $χ$ varies over Dirichlet characters to a prime modulus. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_11664 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Toroidal families and averages of L-functions, I Fouvry, Étienne Kowalski, Emmanuel Michel, Philippe Number Theory 11M06, 11T23, 11A07 We initiate the study of certain families of $L$-functions attached to characters of subgroups of higher-rank tori, and of their average at the central point. In particular, we evaluate the average of the values $L(\demi,χ^a)L(\demi,χ^b)$ for arbitrary integers~$a$ and~$b$ when $χ$ varies over Dirichlet characters to a prime modulus. |
| title | Toroidal families and averages of L-functions, I |
| topic | Number Theory 11M06, 11T23, 11A07 |
| url | https://arxiv.org/abs/2303.11664 |