Rankin-Selberg Convolutions for SO[2l={1 x GL[*n: Local Theory

Erscheinungsjahr 1994
ISBN: 978-0-8218-2568-6
Verlag: American Mathematical Society

Buch, Englisch, 100 Seiten, Format (B × H): 180 mm x 255 mm

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

Autoren/Hrsg.

Soudry, David

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein Grundlagen der Mathematik