Rankin-Selberg Convolutions for So2L+1 X Gln 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 ($l < n$, 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.Soudry, David is the author of 'Rankin-Selberg Convolutions for So2L+1 X Gln Local Theory' with ISBN 9780821825686 and ISBN 0821825682.