EMIS ELibM Electronic Journals PUBLICATIONS DE L'INSTITUT MATHEMATIQUE (BEOGRAD) (N.S.)
Vol. 79(93), pp. 37–49 (2006)

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GITTERPUNKTE IN SUPERKUGELN

Ekkehard Krätzel

Universität Wien, Institut für Mathematik, Nordbergstr. 15, A-1090 Wien, Austria

Abstract: The number of weighted lattice points in a p-dimensional centralsymmetric sphere can be represented by an infinite series over Bessel functions. This is well known. In the present article this result will be generalized to super spheres, which contain points with Gaussian curvature zero at the boundary. In the representation of the number of lattice points in these super spheres the Bessel functions are replaced by convolution products over generalized Bessel functions. These products can be developed into a series over modified generalized Bessel functions. Then one is in the position to prove some new or modified estimates for the number of lattice points inside super spheres.

Keywords: lattice points; convex bodies; super spheres

Classification (MSC2000): 11P21

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Electronic fulltext finalized on: 10 Oct 2006. This page was last modified: 27 Oct 2006.

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