Rankin-Selberg Convolutions for $\mathrm {SO}_{2\ell +1}\times \mathrm {GL}_n$ : Local Theory

This work studies the local theory for certain Rankin-Selberg convolutions for the standard $L$-function of degree $2ln$ of generic representations of ${\rm SO {2\ell+1 (F)\times {\rm GL n(F)$ 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 ($l