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arXiv · 2409.17323

Rankin-Selberg L-Functions for GSpin x GL Groups

Mahdi Asgari·James W. Cogdell·Freydoon Shahidi
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Abstract

We construct an integral representation for the global Rankin-Selberg (partial) $L$-function $L(s, \pi \times \tau)$ where $\pi$ is an irreducible globally generic cuspidal automorphic representation of a general spin group (over an arbitrary number field) and $\tau$ 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 $L(s, \pi \times \tau)$ have, in particular, important consequences in describing the image of the Langlands funtorial transfer from the general spin groups to general linear groups.

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Mahdi Asgari, James W. Cogdell, Freydoon Shahidi. 2024-09-25. Rankin-Selberg L-Functions for GSpin x GL Groups. https://arxiv.org/abs/2409.17323

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