Related papers: Interpolating local constants in families

We define the doubling zeta integral for smooth families of representations of classical groups. Following this we prove a rationality result for these zeta integrals and show that they satisfy a functional equation. Moreover, we show that…

In this article, we construct a family of integrals which represent the product of Rankin-Selberg $L$-functions of $\mathrm{GL}_{l}\times \mathrm{GL}_m$ and of $\mathrm{GL}_{l}\times \mathrm{GL}_n $ when $m+n<l$. When $n=0$, these integrals…

Furusawa has given an integral representation for the degree 8 L-function of GSp(4) x GL(2) and has carried out the unramified calculation. The local p-adic zeta integrals were calculated in our earlier work under the assumption that the…

Let $E$ be a separable quadratic extension of a locally compact field $F$ of positive characteristic. Asai \gamma-factors are defined for smooth irreducible representations \pi of ${\rm GL}_n(E)$. If \sigma is the Weil-Deligne…

Let $F$ be a non-Archimedean local field. Let $\mathcal{A}_n(F)$ be the set of equivalence classes of irreducible admissible representations of $\textrm{GL}_n(F)$, and $\mathcal{G}_n(F)$ be the set of equivalence classes of n-dimensional…

We prove that certain Galois-isotypic parts of the completed cohomology group for U(2) can be written as a completed tensor product of a representation coming from the p-adic Langlands correspondence for $GL_2(\mathbb{Q}_p)$ and a…

The goal of the course was a review of results mainly due to M. Olbrich and the first author. We consider a discrete cocompact subgroup $\Gamma$ of a semisimple Lie group $G$. We relate the group cohomology of $\Gamma$ with coefficients in…

This paper studies Emerton's Jacquet module functor for locally analytic representations of p-adic reductive groups. When P is a parabolic subgroup whose Levi factor M is not commutative, we show that passing to an isotypical subspace for…

We prove that Novodvorsky's definition of local L-factors for generic representations of GSp(4) x GL(2) is compatible with the local Langlands correspondence when the GL(2) representation is non-supercuspidal. We also give an interpretation…

Let $\pi_1,\pi_2$ be a pair of cuspidal complex, or $\ell$-adic, representations of the general linear group of rank $n$ over a non-archimedean local field $F$ of residual characteristic $p$, different to $\ell$. Whenever the local…

In this paper, we construct a family of generalized $L$-functions, one for each point $z$ in the upper half-plane. We prove that as $z$ approaches $i\infty$, these generalized $L$-functions converge to an $L$-function which can be written…

Given a split classical group of symplectic type and a split general linear group over a local field $F$, we use Langlands-Shahidi method to construct their Rankin-Selberg local $\gamma$-factors and prove the corresponding analytic…

In math.RT/0302174 we developed a framework to study representations of groups of the form $G((t))$, where $G$ is an algebraic group over a local field $K$. The main feature of this theory is that natural representations of groups of this…

In this paper, we define a $\gamma$-factor for generic representations of $\RU(1,1)\times \Res_{E/F}(\GL_1)$ and prove a local converse theorem for $\RU(1,1)$ using the $\gamma$-factor we defined. We also give a new proof of the local…

The analytic properties of automorphic L-functions have historically been obtained either through integral representations (the "Rankin-Selberg method"), or properties of the Fourier expansions of Eisenstein series (the "Langlands-Shahidi…

We prove a local converse theorem for $GL_n$ over the archimedean local fields which characterizes an infinitesimal equivalence class of irreducible admissible representations of $GL_n(\mathbb{R})$ or $GL_n(\mathbb{C})$ in terms of twisted…

Let G be a split connected reductive group over a local non-archimedean field. We classify all irreducible complex G-representations in the principal series, irrespective of the (dis)connectedness of the centre of G. This leads to a local…

Let $\pi$ be a simple supercuspidal representation of the quasi-split unramified even unitary group with respect to an unramified quadratic extension $E/F$ of $p$-adic fields. We compute the Rankin-Selberg gamma factor for rank-$1$ twists…

Let G be a locally analytic group and H < G - a locally analytic subgroup. The main result is the condition (similar to Frommer-Orlik-Strauch theorem) for induction of locally analytic H-representation to G to be irreducible. Also this…

Let $X$ be a real prehomogeneous vector space under a reductive group $G$, such that $X$ is an absolutely spherical $G$-variety with affine open orbit. We define local zeta integrals that involve the integration of Schwartz-Bruhat functions…