Results 1 to 10 of about 197 (145)

A non-selfdual automorphic representation of GL3 and a Galois representation

Inventiones Mathematicae, 1994
Given the congruence subgroup \(\Gamma_0 (N)\) of \(\text{SL}_2 (\mathbb Z)\) the first étale cohomology group \(H^1 (X_0 (N)_{\overline {\mathbb Q}}, \mathbb Q_\ell)\) of the associated modular curve \(X_0 (N)\) gives rise to a certain Galois representation (i.e.
Jaap Top
exaly   +5 more sources

On the notion of the parabolic and the cuspidal support of smooth-automorphic forms and smooth-automorphic representations [PDF]

Monatshefte Fur Mathematik
Harald Gröbner, Sonja Žunar
exaly   +2 more sources

New Zero-Density Results for Automorphic L-Functions of GL(n)

Mathematics, 2021
Let L(s,π) be an automorphic L-function of GL(n), where π is an automorphic representation of group GL(n) over rational number field Q. In this paper, we study the zero-density estimates for L(s,π).
Wenjing Ding, Huafeng Liu, Deyu Zhang
doaj   +1 more source

Chow groups and L-derivatives of automorphic motives for unitary groups, II.

Forum of Mathematics, Pi, 2022
In this article, we improve our main results from [LL21] in two directions: First, we allow ramified places in the CM extension $E/F$ at which we consider representations that are spherical with respect to a certain special maximal compact subgroup, by ...
Chao Li, Yifeng Liu
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PERIOD IDENTITIES OF CM FORMS ON QUATERNION ALGEBRAS

Forum of Mathematics, Sigma, 2020
Waldspurger’s formula gives an identity between the norm of a torus period and an $L$-function of the twist of an automorphic representation on GL(2).
CHARLOTTE CHAN
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On fields of rationality for automorphic representations [PDF]

Compositio Mathematica, 2014
Abstract This paper proves two results on the field of rationality $\mathbb{Q}({\it\pi})$ for an automorphic representation
Shin, Sug Woo, Templier, Nicolas
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Raising the level for $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\text {GL}_{{n}}$

Forum of Mathematics, Sigma, 2014
We prove a simple level-raising result for regular algebraic, conjugate self-dual automorphic forms on $\mathrm{GL}_n$ .
JACK A. THORNE
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Representations of automorphism groups on the homology of matroids [PDF]

European Journal of Combinatorics, 2021
Given a group $G$ of automorphisms of a matroid $M$, we describe the representations of $G$ on the homology of the independence complex of the dual matroid $M^*$. These representations are related with the homology of the lattice of flats of $M$, and (when $M$ is realizable) with the top cohomology of a hyperplane arrangement.
Moci Luca, GIan Marco Pezzoli
openaire   +2 more sources

An Integral Representation of Standard Automorphic L Functions for Unitary Groups

International Journal of Mathematics and Mathematical Sciences, 2007
Let F be a number field, G a quasi-split unitary group of rank n. We show that given an irreducible cuspidal automorphic representation π of G(A), its (partial) L function LS(s,π,σ) can be represented by a Rankin-Selberg-type integral involving cusp ...
Yujun Qin
doaj   +1 more source

Rational structures on automorphic representations [PDF]

Mathematische Annalen, 2017
This paper proves the existence of global rational structures on spaces of cusp forms of general reductive groups. We identify cases where the constructed rational structures are optimal, which includes the case of GL($n$). As an application, we deduce the existence of a natural set of periods attached to cuspidal automorphic representations of GL($n$).
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