• An Identity Relating Eisenstein Series on General Linear Groups.
  Z. Hazan. arXiv:2212.00077

Abstract

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).

• A Note on the Asymptotic Expansion of Matrix Coecients over p-Adic Fields. Preprint.
  Z. Hazan. arXiv:2211.15822

Abstract

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.

• On Certain Degenerate Whittaker Models for Cuspidal Representations of GLkn(Fq).
  O. Gorodetsky, Z. Hazan, Mathematische Zeitschrift 291 (2019). arXiv:1707.07308.