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 (2019).
In this short note, presented as a ''community service", followed by the PhD research of the author, we draw the relation between Casselman's theorem regarding the asymptotic behavior of matrix coefficients over p-adic fields and its expression as a finite sum of finite functions.
An Identity Relating Eisenstein Series on General Linear Groups, Number Theory Seminar, UW-Madison (April 21, 2022).
An Identity Relating Eisenstein Series on General Linear Groups, Automorphic Forms Workshop, BYU, Utah (March 19, 2022).
Series of Lectures On Local Gamma Factors for Orthogonal Groups and Unitary Groups, Eisenstein Series Seminar, Tel Aviv University (February 2022).
An Identity Relating Eisenstein Series on General Linear Groups, Algebra and Number Theory Seminar, The University of Arizona (January 25, 2022).
Harmonic analysis over finite fields, TAU Postdoc/graduate student seminar, Tel Aviv University (December 26, 2021).
Mellin Transform over Non-Archimedean Local Fields, Representation Theory Seminar, Tel Aviv University (August 18, 2021).
An Identity Relating Eisenstein Series on General Linear Groups, Algebra and Number Theory Seminar, Yale University (May 11, 2021).