An asymptotic formula for representation of integers by indefinite hermitian forms

LAURET, EMILIO AGUSTÍN

Puerto Natales

Workshop; International Conference on the Algebraic and Arithmetic Theory of Quadratic Forms; 2013

Universidad de Talca

By applying a lattice point theorem on n-dimensional real (and complex) hyperbolic spaces, we gave an asymptotic formula with an error term for the number of integral representations of a negative integer by an indefinite quadratic (and hermitian) forms of signature (n,1). The error term depends on the first nonzero eigenvalue of the LaplaceBeltramioperator in certain hyperbolic manifolds. We also study the behavior of the error term with experimental computations, obtaining evidences on the existence of exceptional eigenvalues in certain complex hyperbolic manifolds.