Related papers: Notes on Analytic Properties of Residual Eisenstei…

We consider the residues at the poles in the right half plane of Eisenstein series, on symplectic groups, or their double covers, induced from Speh representations. We show that for each such pole, there is a unique maximal nilpotent orbit,…

We determine the poles of the Eisenstein series on a general linear group, induced from two Speh representations, $\Delta(\tau,m_1)|\cdot|^s\times\Delta(\tau,m_2)|\cdot|^{-s}$, $Re(s)\geq 0$, where $\tau$ is an irreducible, unitary,…

Let $\mathbb{E}$ be a quadratic extension of a number field $\mathbb{F}$. Let $E(g, s)$ be an Eisenstein series on $GL_2(\mathbb{E})$, and let $F$ be a cuspidal automorphic form on $GL_2(\mathbb{F})$. We will consider in this paper the…

This manuscript has two goals: 1. To write an explicit description of the degenerate residual spectrum of the split, simple, simply-connected, exceptional groups of type $E_n$ (for $n=6,7,8$). 2. To set a practical guide for similar…

In previews works, joint with N. Gurevitch, a family of Rankin-Selberg integrals were shown to represent the twisted standard $\mathcal{L}$-function $\mathcal{L}\left(s,\pi,\chi,\mathfrak{st}\right)$ of a cuspidal representation $ \pi$ of…

In \cite{MR3284482} and \cite{MR3658191}, the twisted standard $\mathcal{L}$-function $\mathcal{L}(s,\pi,\chi,st)$ of a cuspidal representation $ \pi$ of the exceptional group of type $G_2$ was shown to be represented by a family of new-way…

In this paper, we introduce a new family of period integrals attached to irreducible cuspidal automorphic representations $\sigma$ of symplectic groups $\mathrm{Sp}_{2n}(\mathbb{A})$, which detects the right-most pole of the $L$-function…

We study nearly holomorphic Siegel Eisenstein series of general levels and characters on $\mathbb{H}_{2n}$, the Siegel upper half space of degree $2n$. We prove that the Fourier coefficients of these Eisenstein series (once suitably…

Let $\tau_1^{(r)}$, $\tau_2^{(r)}$ be two genuine cuspidal automorphic representations on $r$-fold covers of the adelic points of the general linear groups $GL_{n_1}$, $GL_{n_2}$, resp., and let $E(g,s)$ be the associated Eisenstein series…

Let $G$ be a split group of type $F_4$ defined over a number field. We study the square-integrable automorphic representations of $G$ that can be realized as leading terms of degenerate Eisenstein series associated to various maximal…

Following a strategy suggested by Michel--Venkatesh, we study the cubic moment of automorphic $L$-functions on $\operatorname{PGL}_2$ using regularized diagonal periods of products of Eisenstein series. Our main innovation is to produce…

We study the restriction of the Bump-Friedberg integrals to affine lines $\{(s+\alpha,2s),s\in\C\}$. It has a simple theory, very close to that of the Asai $L$-function. It is an integral representation of the product…

I this paper we determine poles in the right--half plane and images of degenerate Eisenstein series for $GL_n(\Bbb A_\mathbb Q)$ induced from a character on a maximal parabolic subgroup. We apply those results to determine poles of…

We derive a precise relation of poles of Eisenstein series associated to the cuspidal datum $\chi\otimes\sigma$ and the lowest occurrence of theta lifts of a cuspidal automorphic representation $\sigma$ of a unitary group, where $\chi$ is a…

Let $G$ be a linear split algebraic group. The degenerate Eisenstein series associated to a maximal parabolic subgroup $E_{P}(f^{0},s,g)$ with the spherical section $f^{0}$ is studied in the first part of the thesis. In this part, we study…

We consider a certain family of Kudla-Rapoport cycles on an integral model of a Shimura variety attached to a unitary group of signature (1,1), and prove that the arithmetic degrees of these cycles can be identified with the Fourier…

In this paper, we extend Ginzburg-Rallis' integral representation for the exterior cube automorphic $L$-function of ${\rm GL}_6\times {\rm GL}_1$ to that of the quasi-split unitary similitude group ${\rm GU}_6$ and establish its analytic…

If $L(s,\pi)$ and $L(s,\rho)$ are the Dirichlet series attached to cuspidal automorphic representations $\pi$ and $\rho$ of ${\rm GL}_n({\mathbb A}_{\mathbb Q})$ and ${\rm GL}_{n-2}({\mathbb A}_{\mathbb Q})$ respectively, we show that…

We give constraints on the existence of $(\chi,b)$-factors in the global $A$-parameter of a genuine cuspidal automorphic representation $\sigma$ of a metaplectic group in terms of the invariant, lowest occurrence index, of theta lifts to…

The cancellations of poles of degenerate Eisenstein series were studied by Hanzer and Mui\'{c}. This paper generalizes the method and the result to Eisenstein series constructed from inducing two Speh representations…