Rankin-Selberg integrals for ${\mathrm{SO}}_{2n+1}\times {\mathrm{GL}}_r$ attached to Newforms and Oldforms

Abstract

The conjectural newform theory for generic representations of $p$-adic ${\mathrm{SO}}_{2n+1}$ was formulated by P.-Y. Tsai in her thesis in which Tsai also verified the conjecture when the representations are supercuspidal. The main purpose of this work is to compute the Rankin-Selberg integrals for ${\mathrm{SO}}_{2n+1}\times {\mathrm{GL}}_r$ with $1\le r\le n$ attached to newforms and also oldforms under the validity of the conjecture.

Final version. Accepted by Math. Z

References in corpus (1)

• Local Langlands correspondence for $G{L}_n$ and the exterior and symmetric square $\epsilon$--factors