A Note on Counting Cuspidal
نویسنده
چکیده
For geometrically nite Kleinian groups with parabolic elements we study that part of the Lagrange spectrum which does not lie in the Markov spectrum. Using the ergodicity of the associated geodesic ow with respect to the Liouville{Patterson measure, we obtain an estimate for the asymptotic frequency with which recurrent geodesics enter certain cusp regions. In particular, this allows a quantitative description of the logarithmic aanity of geodesic excursions for the cusps.
منابع مشابه
Functoriality for the Exterior Square of Gl4 and the Symmetric Fourth of Gl2
Let ∧ : GLn(C) −→ GLN (C), where N = n(n−1) 2 , be the map given by the exterior square. Then Langlands’ functoriality predicts that there is a map from cuspidal representations of GLn to automorphic representations of GLN , which satisfies certain canonical properties. To explain, let F be a number field, and let A be its ring of adeles. Let π = ⊗ v πv be a cuspidal (automorphic) representatio...
متن کاملWEYL’S LAW FOR THE CUSPIDAL SPECTRUM OF SLn
Let Γ be a principal congruence subgroup of SLn(Z) and let σ be an irreducible unitary representation of SO(n). Let N cus(λ, σ) be the counting function of the eigenvalues of the Casimir operator acting in the space of cusp forms for Γ which transform under SO(n) according to σ. In this paper we prove that the counting function N cus(λ, σ) satisfies Weyl’s law. Especially, this implies that the...
متن کاملDiffeomorphisms, Isotopies, and Braid Monodromy Factorizations of Plane Cuspidal Curves
In this paper we prove that there is an infinite sequence of pairs of plane cuspidal curves Cm,1 and Cm,2, such that the pairs (CP, Cm,1) and (CP, Cm,2) are diffeomorphic, but Cm,1 and Cm,2 have non-equivalent braid monodromy factorizations. These curves give rise to the negative solutions of ”Dif=Def” and ”Dif=Iso” problems for plane irreducible cuspidal curves. In our examples, Cm,1 and Cm,2 ...
متن کاملREDUCTION MODULO p OF CUSPIDAL REPRESENTATIONS AND WEIGHTS IN SERRE’S CONJECTURE
Let O be the ring of integers of a p-adic field and p its maximal ideal. We compute the Jordan-Hölder decomposition of the reduction modulo p of the cuspidal representations of GL2(O/p) for e ≥ 1. We also provide an alternative formulation of Serre’s conjecture for Hilbert modular forms. 1. Cuspidal representations and weights 1.1. Cuspidal representations. Let K/Qp be a local field, where p is...
متن کاملEndoscopy and the cohomology of $GL(n)$
Let $G = {rm Res}_{F/mathbb{Q}}(GL_n)$ where $F$ is a number field. Let $S^G_{K_f}$ denote an ad`elic locally symmetric space for some level structure $K_f.$ Let ${mathcal M}_{mu,{mathbb C}}$ be an algebraic irreducible representation of $G({mathbb R})$ and we let $widetilde{mathcal{M}}_{mu,{mathbb C}}$ denote the associated sheaf on $S^G_{K_f}.$ The aim of this paper is to classify the data ...
متن کامل