Rankin-Selberg convolutions for SO2l+1 x GLn: local theory - 500

This work studies the local theory for certain Rankin-Selberg convolutions for the standard $L$-function of degree $21n$ of generic representations of $\textnormal{SO}_{2\ell +1}(F)\times \textnormal{GL}_n(F)$ over a local field $F$.

The local integrals converge in a half-plane and continue meromorphically to the whole plane.

One main result is the existence of local gamma and $L$-factors.

The gamma factor is obtained as a proportionality factor of a functional equation satisfied by the local integrals.

In addition, Soudry establishes the multiplicativity of the gamma factor ($1<n$, first variable).

A special case of this result yields the unramified computation and involves a new idea not presented before.

This presentation, which contains detailed proofs of the results, is useful to specialists in automorphic forms, representation theory, and $L$-functions, as well as to those in other areas who wish to apply these results or use them in other cases.