Periods detecting Eisenstein series and sums of $L$-values I
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2025
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| _version_ | 1866915553900232704 |
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| author | Lu, Weixiao Xi, Guodong |
| author_facet | Lu, Weixiao Xi, Guodong |
| contents | We study the automorphic period associated to a $G$-Hamiltonian variety $M$ whose dual is $\check{M} = T^*(\check{G}/\check{L})$, where $\check{G}$ is a general linear group and $\check{L}$ is a Levi subgroup. For certain cuspidal Eisenstein series, we prove that their period is equal to a finite sum of special values of $L$-functions. This sum is indexed by the fixed points of the associated extended $L$-parameter on $\check{M}$, confirming a conjecture by Ben-Zvi-Sakellaridis-Venkatesh in this case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_12446 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Periods detecting Eisenstein series and sums of $L$-values I Lu, Weixiao Xi, Guodong Number Theory Representation Theory We study the automorphic period associated to a $G$-Hamiltonian variety $M$ whose dual is $\check{M} = T^*(\check{G}/\check{L})$, where $\check{G}$ is a general linear group and $\check{L}$ is a Levi subgroup. For certain cuspidal Eisenstein series, we prove that their period is equal to a finite sum of special values of $L$-functions. This sum is indexed by the fixed points of the associated extended $L$-parameter on $\check{M}$, confirming a conjecture by Ben-Zvi-Sakellaridis-Venkatesh in this case. |
| title | Periods detecting Eisenstein series and sums of $L$-values I |
| topic | Number Theory Representation Theory |
| url | https://arxiv.org/abs/2510.12446 |