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L-functions for $$SO_ n\times GL_ k$$. (English) Zbl 0684.22009
We prove Langlands’ conjecture for the standard representation of the groups $$SO_{2n+1}\times GL_ k$$ and $$SO_{2n}\times GL_ k$$ where $$k<n$$. We construct Rankin-Selberg integrals for these groups, prove their convergence, show that they are Euclidean and compute the unramified local integrals. These integrals are a natural generalization of the ones constructed for $$SO_{2n+1}\times GL_ n$$ and $$SO_{2n}\times GL_ n$$ be Gelbart and Piatetski-Shapiro.
Reviewer: D.Ginzburg

##### MSC:
 22E55 Representations of Lie and linear algebraic groups over global fields and adèle rings 11F70 Representation-theoretic methods; automorphic representations over local and global fields 11R39 Langlands-Weil conjectures, nonabelian class field theory 11M06 $$\zeta (s)$$ and $$L(s, \chi)$$ 11R42 Zeta functions and $$L$$-functions of number fields
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