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A Product of Tensor Product $L$-functions of Quasi-split Classical Groups of Hermitian Type | | Dihua Jiang
; Lei Zhang
; | | Date: |
29 Dec 2012 | | Abstract: | A family of global integrals representing a product of tensor product
(partial) $L$-functions: $ L^S(s,pi imes au_1)L^S(s,pi imes au_2)...
L^S(s,pi imes au_r) $ are established in this paper, where $pi$ is an
irreducible cuspidal automorphic representation of a quasi-split classical
group of Hermitian type and $ au_1,..., au_r$ are irreducible unitary
cuspidal automorphic representations of $GL_{a_1},...,GL_{a_r}$,
respectively. When $r=1$ and the classical group is an orthogonal group, this
was studied by Ginzburg, Piatetski-Shapiro and Rallis in 1997 and when $pi$ is
generic and $ au_1,..., au_r$ are not isomorphic to each other, this is
considered by Ginzburg, Rallis and Soudry in 2011. In this paper, we prove that
the global integrals are eulerian and finish the explicit calculation of
unramified local $L$-factors in general. The remaining local and global theory
for this family of global integrals will be considered in our future work. | | Source: | arXiv, 1212.6580 | | Services: | Forum | Review | PDF | Favorites | |
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