相关论文: Rankin-Selberg integrals for local symmetric squar…

We prove the classical $l = p$ local-global compatibility conjecture for certain regular algebraic cuspidal automorphic representations of weight 0 for GL$_2$ over CM fields. Using an automorphy lifting theorem, we show that if the…

Given a cuspidal automorphic form $\pi$ on $\GL_2$, we study smoothed sums of the form $\sum_{n\in\mathbb{N}} a_{\pi}(n^2+d)W(\frac{n}{Y})$. The error term we get is sharp in that it is uniform in both $d$ and $Y$ and depends directly on…

Let $G$ be a simply connected, connected completely solvable Lie group with Lie algebra $\mathfrak{g}=\mathfrak{p}+\mathfrak{m}.$ Next, let $\pi$ be an infinite-dimensional unitary irreducible representation of $G$ obtained by inducing a…

We refine and extend previous constructions of $p$-adic $L$-functions for Rankin-Selberg convolutions on $\GL(n)\times\GL(n-1)$ for regular algebraic representations over totally real fields. We also prove an intrinsic functional equation…

For $m\ge 2$, let $\pi$ be an irreducible cuspidal automorphic representation of $GL_m(\mathbb{A}_{\mathbb{Q}})$ with unitary central character. Let $a_\pi(n)$ be the $n^{th}$ coefficient of the $L$-function attached to $\pi$. Goldfeld and…

In this note we prove a quantitative stability result for the $\epsilon$-factors associated to generic irreducible representations of $\textrm{GL}_n(F)$ under twists by highly ramified characters, where $F$ is a non-archimedean local field.

Let $\pi=\otimes\pi_{v}$ and $\pi^{\prime}=\otimes\pi_{v}^{\prime}$ be two irreducible, automorphic, cuspidal representations of $GL_{m}(\mathbb{A}_{K}) >.$ Using the logarithmic zero-free region of Rankin-Selberg $L$-function, Moreno…

Let $\pi$ and $\pi'$ be cuspidal automorphic representations of $\mathrm{GL}(n)$ and $\mathrm{GL}(n')$ with unitary central characters. We establish a new zero-free region for all $\mathrm{GL}(1)$-twists of the Rankin-Selberg $L$-function…

Let $F$ be a local field of characteristic $p>0$. By adapting methods of Scholze, we give a new proof of the local Langlands correspondence for $\GL_n$ over $F$. More specifically, we construct $\ell$-adic Galois representations associated…

We study Artin $L$-functions on a finite $2$-dimensional complex $X_\Gamma$ arising from PGL$_3$ attached to finite-dimensional representations $\rho$ of its fundamental group. Some key properties, such as rationality, functional equation,…

From a spectral identity we obtain asymptotics with error term for the second integral moments of families of automorphic L-functions for GL(2) over an arbitrary number field according to twists by idele characters with arbitrary…

Using the ideas of Deninger, we prove that the Artin $L$-functions coincide with such of the noncommutative tori. This result can be viewed as the Langlands reciprocity for noncommutative tori.

We obtain an upper bound for the dimension of the cuspidal automorphic forms for $\mathrm{GL}_2$ over a number field, whose archimedean local representations are not tempered. More precisely, we prove the following result. Let $F$ be a…

Rallis and Soudry have proven the stability under twists by highly ramified characters of the local gamma factor arising from the doubling method, in the case of a symplectic group or orthogonal group G over a local non-archimedean field F…

In this paper, we give a precise definition of the analytic $\gamma$-factors of irreducible representations of quaternionic unitary groups, which extends a work of Lapid-Rallis.

Let $K/F$ be a quadratic extension of $p$-adic fields, $\sigma$ the nontrivial element of the Galois group of $K$ over $F$, and $\pi$ a quasi-square-integrable representation of $GL(n,K)$. Denoting by $\pi^{\vee}$ the smooth contragredient…

We prove explicit rationality-results for Asai- $L$-functions, $L^S(s,\Pi',{\rm As}^\pm)$, and Rankin-Selberg $L$-functions, $L^S(s,\Pi\times\Pi')$, over arbitrary CM-fields $F$, relating critical values to explicit powers of $(2\pi i)$.…

It is conjectured by Adams-Vogan and Prasad that under the local Langlands correspondence, the L-parameter of the contragredient representation equals that of the original representation composed with the Chevalley involution of the…

Let $\rk$ be a local field of characteristic zero. Let $\pi$ be an irreducible admissible smooth representation of $\GL_{2n}(\rk)$. We prove that for all but countably many characters $\chi$ of $\GL_n(\rk)\times \GL_n(\rk)$, the space of…

Let $K$ be a non-archimedean local field and let $G = \mathrm{GL}_n(K)$. We have shown in previous work that the smooth dual $\mathbf{Irr}(G)$ admits a complex structure: in this article we show how the epsilon factors interface with this…