Rankin-Selberg Convolutions for SO2 1 GLn

Local Theory

David Soudry (Autor)

Buch | Softcover

100 Seiten

1993
American Mathematical Society (Verlag)
978-0-8218-2568-6 (ISBN)

Infos

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 $F$. This book is suitable for specialists in automorphic forms, representation theory, and $L$-functions.

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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

Inhalt

Introduction and preliminaries The integrals to be studied Estimates for Whittaker functions on $G_/ell$ (nonarchimedean case) Estimates for Whittaker functions on $G_/ell$ (archimedean case) Convergence of the integrals (nonarchimedean case) Convergence of the integrals (archimedean case) $A(W,/xi_{/tau,s})$ can be made constant (nonarchimedean case) An analog in the archimedean case Uniqueness theorems Application of the intertwining operator Definition of local factors Multiplicativity of the $/gamma$-factor (case $/ell < n$, first variable) The unramified computation.

Produkt-Details

• Erscheint lt. Verlag: 30.9.1993
• Reihe/Serie: Memoirs of the American Mathematical Society
• Verlagsort: Providence
• Sprache: englisch
• Gewicht: 227 g
• Themenwelt: Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre
• ISBN-10: 0-8218-2568-2 / 0821825682
• ISBN-13: 978-0-8218-2568-6 / 9780821825686
• Zustand: Neuware