Rankin-Selberg L-Functions for GSpin x GL Groups
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866914957329694720 |
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| author | Asgari, Mahdi Cogdell, James W. Shahidi, Freydoon |
| author_facet | Asgari, Mahdi Cogdell, James W. Shahidi, Freydoon |
| contents | We construct an integral representation for the global Rankin-Selberg (partial) $L$-function $L(s, π\times τ)$ where $π$ is an irreducible globally generic cuspidal automorphic representation of a general spin group (over an arbitrary number field) and $τ$ is one of a general linear group, generalizing the works of Gelbart, Piatetski-Shapiro, Rallis, Ginzburg, Soudry and Kaplan among others. We consider all ranks and both even and odd general spin groups including the quasi-split forms. The resulting facts about the location of poles of $L(s, π\times τ)$ have, in particular, important consequences in describing the image of the Langlands funtorial transfer from the general spin groups to general linear groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_17323 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Rankin-Selberg L-Functions for GSpin x GL Groups Asgari, Mahdi Cogdell, James W. Shahidi, Freydoon Number Theory Representation Theory 11F70, 11F66, 22E50, 22E55, We construct an integral representation for the global Rankin-Selberg (partial) $L$-function $L(s, π\times τ)$ where $π$ is an irreducible globally generic cuspidal automorphic representation of a general spin group (over an arbitrary number field) and $τ$ is one of a general linear group, generalizing the works of Gelbart, Piatetski-Shapiro, Rallis, Ginzburg, Soudry and Kaplan among others. We consider all ranks and both even and odd general spin groups including the quasi-split forms. The resulting facts about the location of poles of $L(s, π\times τ)$ have, in particular, important consequences in describing the image of the Langlands funtorial transfer from the general spin groups to general linear groups. |
| title | Rankin-Selberg L-Functions for GSpin x GL Groups |
| topic | Number Theory Representation Theory 11F70, 11F66, 22E50, 22E55, |
| url | https://arxiv.org/abs/2409.17323 |