Rankin-Selberg Convolutions for SO[2l={1 x GL[*n: Local Theory - Soudry, David
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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 …mehr

Produktbeschreibung
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.

This book presents two new ideas: the justification of formal manipulations in the proof of multiplicativity of the gamma factor, through a uniqueness principle, and the use of a key identity in this proof to reduce the unramified computation in the case l