On a Lattice Problem for Geodesic Double Differential Forms in the -Dimensional Hyperbolic Space
Reinhard Schuster
Universität Leipzig, Germany
![On a Lattice Problem for Geodesic Double Differential Forms in the $n$-Dimensional Hyperbolic Space cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-zaa-volume-9-issue-6.png&w=3840&q=90)
Abstract
Generalizing a lattice point problem we solve a lattice problem for geodesic double differential forms in the -dimensional hyperbolic space. Thereby we use a properly discontinuous group of isometrics of with compact fundamental domain. We study the relation between lattice sums and the eigenvalue spectrum of the Laplace operator for -forms on the hyperbolic space form . Our approach essentially uses mean value operators for differential forms, their kernel double differential forms and a Landau difference method.
Cite this article
Reinhard Schuster, On a Lattice Problem for Geodesic Double Differential Forms in the -Dimensional Hyperbolic Space. Z. Anal. Anwend. 9 (1990), no. 6, pp. 519–534
DOI 10.4171/ZAA/421