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...
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We investigate the connection between integral weight and half-integral weight modular forms. Building on results of Ueda 14], we obtain structure theorems for spaces of half-integral weight cusp forms S k=2 (4N;) where k and N are odd nonnegative integers with k 3, and is an even quadratic Dirichlet character modulo 4N. We give complete results in the case where N is a power of a single prime,...
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We introduce and describe one-dimensional cyclotomic Gauss-Selberg sums generalizing the classical Gaussian sums. They correspond to irreducible self-dual unitary spherical representations of the one-dimensional double affine Hecke algebra. Introduction This paper is about applications of the one-dimensional double affine Hecke algebra to q-Gauss integrals and Gaussian sums. The double affine H...
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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...
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1 The affine Hecke algebra 1.1 The alcove walk algebra Fix notations for the Weyl group W , the extended affine Weyl group W , and their action on Ω × h * R as in Section 2. Label the walls of the alcoves so that the fundamental alcove has walls labeled 0, 1,. .. , n and the labeling is W-equivariant (see the picture in (2.12)). The periodic orientation is the orientation of the walls of the al...
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ژورنال
عنوان ژورنال: Experimental Mathematics
سال: 2018
ISSN: 1058-6458,1944-950X
DOI: 10.1080/10586458.2017.1409144