Letbe a Salem number of degree d with 4 6 d 6 18. We show that if d Á 0; 4 or 6. mod 8/, then
is the dynamical degree of an automorphism of a complex (non-projective) K3 surface. We …

We characterize the irreducible polynomials that occur as the characteristic polynomial of an
automorphism of an even unimodular lattice of a given signature, generalizing a theorem of …

We apply G. Prasad's volume formula for the arithmetic quotients of semi-simple groups and
Bruhat-Tits theory to study the covolumes of arithmetic subgroups of SO (1, n). As a result we …

In this paper we derive an explicit formula for the Hirzebruch-Mumford volume of an
indefinite lattice L of rank≥ 3. If Γ⊂ O (L) is an arithmetic subgroup and L has signature (2 …

We compute the Zamolodchikov volumes of some moduli spaces of conformal field theories
with target spaces K3, T4, and their symmetric products. As an application we argue that …

Abstract The celebrated Smith–Minkowski–Siegel mass formula expresses the mass of a
quadratic lattice (L, Q) as a product of local factors, called the local densities of (L, Q). This …

Suppose Q is a definite quadratic form on a vector space V over some totally real field K≠ Q.
Then the maximal integral Z K-lattices in (V, Q) are locally isometric everywhere and hence …

Let X be a complex projective K3 surface and let\(T_X\) be its transcendental lattice; the
characteristic polynomials of isometries of\(T_X\) induced by automorphisms of X are powers …

This paper is a follow-up to the paper I. Agol, M. Belolipetsky, P. Storm, K. Whyte, Finiteness
of arithmetic hyperbolic reflection groups, Groups, Geometry, and Dynamics 2 (2008), 481 …

Let X be a complex projective K3 surface, and let T (X) be its transcendental lattice; the
characteristic polynomials of the isometries of T (X) induced by automorphisms of X are …