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Analytic properties of zeta functions and subgroup growth
It has become somewhat of a cottage industry over the last fifteen years to understand the rate of growth of the number of subgroups of finite index in a group G. Although the story began much
Beauville surfaces without real structures
Inspired by a construction by Arnaud Beauville of a surface of general type with K 2 = 8, p g = 0, the second author defined Beauville surfaces as the surfaces which are rigid, i.e., without
Linear Representations of the Automorphism Group of a Free Group
Abstract.Let Fn be the free group on n ≥ 2 elements and Aut(Fn) its group of automorphisms. In this paper we present a rich collection of linear representations of Aut(Fn) arising through the action
Groups Acting on Hyperbolic Space: Harmonic Analysis and Number Theory
1. Three-Dimensional Hyperbolic Space.- 2. Groups Acting Discontinuously on Three-Dimensional Hyperbolic Space.- 3. Automorphic Functions.- 4. Spectral Theory of the Laplace Operator.- 5. Spectral
The classification of surfaces with p_g = q = 0 isogenous to a product of curves
We classify all the surfaces with p_g = q = 0 which admit an unramified covering which is isomorphic to a product of curves. Beyond the trivial case \PP^1 x \PP^1 we find 17 families which we
Quotients of products of curves, new surfaces with pg = 0 and their fundamental groups.
We construct many new surfaces of general type with $q=p_g = 0$ whose canonical model is the quotient of the product of two curves by the action of a finite group $G$, constructing in this way many
Zeta functions of groups and rings
We report on progress and problems concerning the analytical behaviour of the zeta functions of groups and rings. We also describe how these generating functions are special cases of adelic cone