Rankin-Selberg integrals for $\mathrm{GSpin}$ groups with application to the global Gan-Gross-Prasad conjecture
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916893974069248 |
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| author | Yan, Pan |
| author_facet | Yan, Pan |
| contents | We construct Rankin-Selberg integrals using Bessel models for a product of tensor product partial $L$-functions \begin{equation*} L^S(s,π\timesτ_1) L^S(s,π\timesτ_2)\cdots L^S(s,π\timesτ_r) \end{equation*} where $π$ is an irreducible cuspidal automorphic representation of a quasi-split $\mathrm{GSpin}$ group, and $τ_1, \cdots, τ_r$ are irreducible unitary cuspidal automorphic representations of $\mathrm{GL}_{k_1}, \cdots, \mathrm{GL}_{k_r}$ respectively. As an application, we prove one direction of the global Gan-Gross-Prasad conjecture for generic representations of quasi-split $\mathrm{GSpin}$ groups. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_09066 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rankin-Selberg integrals for $\mathrm{GSpin}$ groups with application to the global Gan-Gross-Prasad conjecture Yan, Pan Number Theory Representation Theory Primary 11F70, Secondary 11F67, 11F66, 22E55 We construct Rankin-Selberg integrals using Bessel models for a product of tensor product partial $L$-functions \begin{equation*} L^S(s,π\timesτ_1) L^S(s,π\timesτ_2)\cdots L^S(s,π\timesτ_r) \end{equation*} where $π$ is an irreducible cuspidal automorphic representation of a quasi-split $\mathrm{GSpin}$ group, and $τ_1, \cdots, τ_r$ are irreducible unitary cuspidal automorphic representations of $\mathrm{GL}_{k_1}, \cdots, \mathrm{GL}_{k_r}$ respectively. As an application, we prove one direction of the global Gan-Gross-Prasad conjecture for generic representations of quasi-split $\mathrm{GSpin}$ groups. |
| title | Rankin-Selberg integrals for $\mathrm{GSpin}$ groups with application to the global Gan-Gross-Prasad conjecture |
| topic | Number Theory Representation Theory Primary 11F70, Secondary 11F67, 11F66, 22E55 |
| url | https://arxiv.org/abs/2508.09066 |