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A sum formula related to ellipsoids with applications to lattice point theory

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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.

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Author information

Correspondence to E. Krätzel.

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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

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Keywords

  • Asymptotic Expansion
  • Lattice Point
  • Asymptotic Representation
  • Series Representation
  • Infinite Series