Rankin-Selberg Convolutions for So2L+1 X Gln: Local Theory (Memoirs of the American Mathematical Society)
( Memoirs of the American Mathematical Society )
Publication series ：Memoirs of the American Mathematical Society
Author： David Soudry
Publisher： American Mathematical Society
Publication year： 2013
E-ISBN: 9781470400774
P-ISBN(Paperback): 9780821825686
Subject： O17 Mathematical Analysis
Keyword： Number Theory
Language： ENG
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Rankin-Selberg Convolutions for So2L+1 X Gln: Local Theory (Memoirs of the American Mathematical Society)
Description
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