Rankin-Selberg convolutions for SO[2l+1] × GL[n] : local theory
著者
書誌事項
Rankin-Selberg convolutions for SO[2l+1] × GL[n] : local theory
（Memoirs of the American Mathematical Society, no. 500）
American Mathematical Society, 1993
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Rankin-Selberg convolutions for SO2l+1 x GLn : local theory
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注記
"September 1993, volume 105, number 500 (first of 6 numbers)"
Includes bibliographical references (p. 99-100)
内容説明・目次
内容説明
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
目次
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.
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