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Zeitschrift für Analysis und ihre Anwendungen


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Volume 9, Issue 6, 1990, pp. 519–534
DOI: 10.4171/ZAA/421

Published online: 1990-12-31

On a Lattice Problem for Geodesic Double Differential Forms in the $n$-Dimensional Hyperbolic Space

Reinhard Schuster[1]

(1) Universität Leipzig, Germany

Generalizing a lattice point problem we solve a lattice problem for geodesic double differential forms in the $n$-dimensional hyperbolic space. Thereby we use a properly discontinuous group $\mathfrak G$ of isometrics of $\mathbb H_n$ with compact fundamental domain. We study the relation between lattice sums and the eigenvalue spectrum of the Laplace operator for $p$-forms on the hyperbolic space form $\mathbb H_n/\mathfrak G$. Our approach essentially uses mean value operators for differential forms, their kernel double differential forms and a Landau difference method.

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Schuster Reinhard: On a Lattice Problem for Geodesic Double Differential Forms in the $n$-Dimensional Hyperbolic Space. Z. Anal. Anwend. 9 (1990), 519-534. doi: 10.4171/ZAA/421