منابع مشابه
Companion forms and weight one forms
We have three motivations for looking at this theorem. Firstly it can be seen as partial confirmation of a conjecture of Fontaine and Mazur which asserts that if ρ : GQ → GLn(Qp) is a continuous irreducible representation ramified at only finitely many primes and such that the image of the inertia group at p is finite, then the image of ρ is finite (see [FM]). Our theorem verifies this conjectu...
متن کاملModular Forms of Weight One
The decomposition into an Euler product and the functional equation of the Dirichlet series associated by Hecke to modular forms of weight one suggests that these correspond to Artin L-functions of degree 2 over Q, otherwise known as Galois representations Gal(Q/Q)→ GL2(C). It is this correspondence, conjectured by Langlands, which we establish here. The first three sections are preliminary. Th...
متن کاملMock-modular Forms of Weight One
The object of this paper is to initiate a study of the Fourier coefficients of a weight one mock-modular form and relate them to the complex Galois representations associated to the form’s shadow, which is a weight one newform. In this paper, our focus will be on weight one dihedral newforms of prime level p ≡ 3 (mod 4). In this case we give properties of the Fourier coefficients themselves tha...
متن کاملHarmonic Maass Forms of Weight One
The object of this paper is to initiate a study of the Fourier coefficients of a weight one harmonic Maass form and relate them to the complex Galois representation associated to a weight one newform, which is the form’s image under a certain differential operator. In this paper, our focus will be on weight one dihedral newforms of prime level p ≡ 3 (mod 4). In this case we give properties of t...
متن کاملCompanion Forms for Unitary and Symplectic Groups
We prove a companion forms theorem for ordinary n-dimensional automorphic Galois representations, by use of automorphy lifting theorems developed by the second author, and a technique for deducing companion forms theorems due to the first author. We deduce results about the possible Serre weights of mod l Galois representations corresponding to automorphic representations on unitary groups. We ...
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ژورنال
عنوان ژورنال: The Annals of Mathematics
سال: 1999
ISSN: 0003-486X
DOI: 10.2307/121076