Zahi Hazan
Published 2022-11-30Version 1
We give a general identity relating Eisenstein series on general linear groups. We do it by constructing an Eisenstein series, attached to a maximal parabolic subgroup and a pair of representations, one cuspidal and the other a character, and express it in terms of a degenerate Eisenstein series. In the local fields analogue, we prove the convergence in a half plane of the local integrals, and their meromorphic continuation. In addition, we find that the unramified calculation gives the Godement-Jacquet zeta function. This realizes and generalizes the construction proposed by Ginzburg and Soudry in Section 3 in their aritcle "Integral derived from the doubling method".
Generalized Bump-Hoffstein conjecture for coverings of general linear groups
On the images and poles of degenerate Eisenstein series for $GL_n(\mathbb A_{\mathbb Q})$ and $GL_n(\mathbb R)$
On Unfoldings of Some Integrals of Automorphic Functions on General Linear Groups
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