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Beyond the extended Selberg class: $1<d_F< 2$
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abstract
We show that a class of Dirichlet series ${\mathfrak{A}}^{\#}$ that is much larger than the extended Selberg class ${\mathscr{S}}^{\#}$, and also contains the standard as well as the tensor product, exterior square and symmetric square $L$-functions of automorphic $L$-functions of $GL_n$ over number fields, does not have any elements of degrees between $1$ and $2$. The proof of our more general theorem is very different from the proof of Kaczorowski and Perelli for the class ${\mathscr{S}}^{\#}$, and is much shorter and simpler even in that case.
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Cited by 1 Pith paper
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On the exterior square $\varepsilon$-factors of $GL_n$
For generic representations of GL_r over a p-adic field, the Jacquet-Shalika and Langlands-Shahidi exterior-square epsilon factors coincide.
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