Abstract
In this article we consider finite and infinitep-dimensional sums over functionsf, where the argument off is represented by a positive definite quadratic form. We develop a sum formula like theEuler-Maclaurin orPoisson sum formula. Applications to exponential sums and lattice point problems are given.
Similar content being viewed by others
References
H. Bateman andA. Erdelyi,Higher Transcendental Functions II. Mc Graw-Hill Book Company, Inc., New York, Toronto, London, 1953.
—,Tables of Integral Transforms 1. Mc Graw-Hill Book Company, Inc., New York, Toronto, London, 1954.
E. T. Copson,Asymptotic Expansions. At the University Press, Cambridge, 1965.
G. Doetsch.Handbuch der Laplace-Transformation II. Birkhäuser, Basel, 1953.
E. Krätzel,Lattice Points. Dt. Verlag d. Wiss., Berlin und Kluwer Academic Publishers Dordrecht, Boston, London, 1988.
E. Landau, Über eine Aufgabe aus der Theorie der quadratischen Formen,Sitzungsberichte d. kaiserl. Akad. d. Wiss. Wien, math.-naturwiss. Klasse 124 (1915), 445–468.
—, Die Bedeutungslosigkeit der Pfeiffer’schen Methode für die analytische Zahlentheorie,Monatsh. f. Math. u. Phys. 34 (1925), 1–36.
A. Walfisz,Ausgewählte Abhandlungen zur Gitterpunktlehre von Edmund Landau. DVW, Berlin, 1962.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Krätzel, E. A sum formula related to ellipsoids with applications to lattice point theory. Abh.Math.Semin.Univ.Hambg. 71, 143–159 (2001). https://doi.org/10.1007/BF02941468
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02941468