Toroidal families and averages of $L$-functions, II: cubic moments
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866908879073312768 |
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| author | Fouvry, Étienne Kowalski, Emmanuel Michel, Philippe Sawin, Will |
| author_facet | Fouvry, Étienne Kowalski, Emmanuel Michel, Philippe Sawin, Will |
| contents | Generalizing our previous work on ``toroidal averages'', we study the average of special values of $L$-functions of the form $L(1/2,χ^a)L(1/2,χ^b)L(1/2,χ^c)$ for integers $a$, $b$ and $c$, where $χ$ varies over Dirichlet characters of a given prime modulus. We highlight connections with estimates for bilinear forms of trace functions and with bounds for the number of solutions of monoidal equations in three variables in small boxes over finite fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_10746 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Toroidal families and averages of $L$-functions, II: cubic moments Fouvry, Étienne Kowalski, Emmanuel Michel, Philippe Sawin, Will Number Theory 11T23, 11L05, 11Mxx, 11N37, 11N75, 11F66, 14F20, 14D05 Generalizing our previous work on ``toroidal averages'', we study the average of special values of $L$-functions of the form $L(1/2,χ^a)L(1/2,χ^b)L(1/2,χ^c)$ for integers $a$, $b$ and $c$, where $χ$ varies over Dirichlet characters of a given prime modulus. We highlight connections with estimates for bilinear forms of trace functions and with bounds for the number of solutions of monoidal equations in three variables in small boxes over finite fields. |
| title | Toroidal families and averages of $L$-functions, II: cubic moments |
| topic | Number Theory 11T23, 11L05, 11Mxx, 11N37, 11N75, 11F66, 14F20, 14D05 |
| url | https://arxiv.org/abs/2603.10746 |