arXiv subjects

David Soudry

Publications and source records attributed to David Soudry.

9 recordsLinked to original sources

arXiv2024

Poles of Eisenstein series on general linear groups induced from two Speh representations

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, cuspidal, automorphic representation of $GL_n({\bf A})$. The poles are simple and occur at $s=\frac{m_1+m_2}{4}-\frac{i}{2}$, $0\leq i\leq min(m_1,m_2)-1$. Our methods also show that when $m_1=m_2$, the above Eisenstein series vanish at s=0.

math.RT↗

arXiv2023

On gamma factors for representations of finite general linear groups

We use the Langlands--Shahidi method in order to define the Shahidi gamma factor for a pair of irreducible generic representations of $\operatorname{GL}_n\left(\mathbb{F}_q\right)$ and $\operatorname{GL}_m\left(\mathbb{F}_q\right)$. We prove that the Shahidi gamma factor is multiplicative and show that it is related to the Jacquet--Piatetski-Shapiro--Shalika gamma factor. As an application, we prove a converse theorem based on the absolute value of the Shahidi gamma factor, and improve the converse theorem of Nien. As another application, we give explicit formulas for special values of the Bessel function of an irreducible generic representation of $\operatorname{GL}_n\left(\mathbb{F}_q\right)$.

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arXiv2022

A new regularized Siegel-Weil type formula, part I

In this paper, we propose a formula relating certain residues of Eisenstein series on symplectic groups. These Eisenstein series are attached to parabolic data coming from Speh representations. The proposed formula bears a strong similarity to the regularized Siegel-Weil formula, established by Kudla and Rallis for symplectic-orthogonal dual pairs. Their work was later generalized by Ikeda, Moeglin, Ichino, Yamana, Gan-Qiu-Takeda and others.

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arXiv2020

Top Fourier coefficients of residual Eisenstein series on symplectic or metaplectic groups induced from Speh representations

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, attached to Fourier coefficients admitted by the corresponding residual representation. We find this orbit in each case.

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arXiv2020

Double Descent in Classical Groups

Let ${\bf A}$ be the ring of adeles of a number field $F$. Given a self-dual irreducible, automorphic, cuspidal representation $\tau$ of $\GL_n(\BA)$, with trivial central characters, we construct its full inverse image under the weak Langlands functorial lift from the appropriate split classical group $G$. We do this by a new automorphic descent method, namely the double descent. This method is derived from the recent generalized doubling integrals of Cai, Friedberg, Ginzburg and Kaplan \cite{CFGK17}, which represent the standard $L$-functions for $G\times \GL_n$. Our results are valid also for double covers of symplectic groups.

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arXiv2018

Integrals derived from the doubling method

In this note, we use a basic identity, derived from the generalized doubling integrals of \cite{C-F-G-K1}, in order to explain the existence of various global Rankin-Selberg integrals for certain $L$-functions. To derive these global integrals, we use the identities relating Eisenstein series in \cite{G-S}, together with the process of exchanging roots. We concentrate on several well known examples, and explain how to obtain them from the basic identity. Using these ideas, we also show how to derive a new global integral.

math.NT↗

arXiv2018

Two Identities relating Eisenstein series on classical groups

In this paper we introduce two general identities relating Eisenstein series on split classical groups, as well as double covers of symplectic groups. The first identity can be viewed as an extension of the doubling construction introduced in [CFGK17]. The second identity is a generalization of the descent construction studied in [GRS11].

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arXiv2004

The local converse theorem for SO(2n+1) and applications

In this paper we characterize irreducible generic representations of $\SO_{2n+1}(k)$ where $k$ is a $p$-adic field) by means of twisted local gamma factors (the Local Converse Theorem). As applications, we prove that two irreducible generic cuspidal automorphic representations of $\SO_{2n+1}({\Bbb A})$ (where ${\Bbb A}$ is the ring of adeles of a number field) are equivalent if their local components are equivalent at almost all local places (the Rigidity Theorem);and prove the Local Langlands Reciprocity Conjecture for generic supercuspidal representations of $\SO_{2n+1}(k)$.

math.RT↗

arXiv1999

On explicit lifts of cusp forms from GL_m to classical groups

In this paper, we begin the study of poles of partial L-functions L^S(sigma tensor tau,s), where sigma tensor tau is an irreducible, automorphic, cuspidal, generic (i.e. with nontrivial Whittaker coefficient) representation of G_A x GL_m(A). G is a split classical group and A is the adele ring of a number field F. We also consider tilde{Sp}_{2n}(A) x GL_m(A), where tilde denotes the metaplectic cover.

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