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 quantita...

Throughout this paper, G denotes a fixed. not necessarily connected, reductive algebraic group over an algebraically closed field k. This paper is a part of a series (beginning with [L10], [L11], [L12]) which attempts to develop a theory of character sheaves on G. The numbering of the sections and references continues that of the earlier Parts. Assume that k is an algebraic closure of a finite ...

The goal of this paper is to establish the regularity of the solution of the first initial-boundary value problem for general higher-order hyperbolic equations in cylinders with the bases containing cuspidal points.

Let p be an odd prime, and let q be a power of p. Let G = Sp(4). B.Srinivasan (in [4]) discovered an irreducible representation (denoted by θ10) of Sp(4,Fq) with the following remarkable combination of properties, namely it is cuspidal(Defn. 4.1), unipotent(Defn. 5.8) as well as degenerate, i.e. it does not admit a Whittaker model(Defn. 4.2). The groups SLn(Fq) and GLn(Fq) do not have any unipo...