A Lattice Problem for Differential Forms in Euclidean Spaces

Abstract

Generalizing a lattice-point problem we solve a lattice problem for $\mathfrak{G}$-automorphic differential $p$-forms in the $n$-dimensional Euclidean space ${\mathbf{E}}^n$, where $\mathfrak{G}$ is a properly discontinuous group of isometrics of ${\mathbf{E}}^n$ with compact fundamental domain. Our approach essentially uses mean value operators for differential forms and a Landau difference method.