Explicit formulas for the Bessel models: odd general spin groups

Abstract Let F be a non-archimedean local field of characteristic zero. In this work, we study the Bessel model for $$\operatorname {GSpin}_{2n+1}$$ GSpin 2 n + 1 , extending a result of Bump, Friedberg and Furusawa [6]. 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 $$\operatorname {GSpin}_{2n+1} \times \operatorname {GL}_n$$ GSpin 2 n + 1 × 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 [3], specifically in their unramified computation.