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arXiv · 2509.03278

Explicit formulas for the Bessel models: odd general spin groups

Yu Xin
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Abstract

Let $F$ be a non-archimedean local field of characteristic zero. In this work, we study the Bessel model for $\GSpin_{2n+1}$, extending a result of Bump, Friedberg and Furusawa. In particular, we obtain explicit formulas for the unramified Bessel functions. These formulas have a global application to a Rankin--Selberg integral of the $L$-function for $\GSpin_{2n+1} \times \GL_n$, generalizing a construction of Furusawa. We compute the local factor of the global integral at a good place. Moreover, a corollary of this computation finds an application in a recent work of Asgari, Cogdell and Shahidi, specifically in their unramified computation.

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Yu Xin. 2025-09-03. Explicit formulas for the Bessel models: odd general spin groups. https://arxiv.org/abs/2509.03278

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