An integral formula for the number of lattice points in a domain

Lev Aizenberg; Nikolai Tarkhanov

doi:10.17516/1997-1397-2015-8-2-134-139

An integral formula for the number of lattice points in a domain

Lev Aizenberg
, Nikolai Tarkhanov

Department of Mathematics

University of Potsdam

Research output: Contribution to journal › Article › peer-review

Abstract

Using the multidimensional logarithmic residue we show a simple formula for the difference between the number of integer points in a bounded domain of Rn and the volume of this domain. The difference proves to be the integral of an explicit differential form over the boundary of the domain.

Original language	English
Pages (from-to)	134-139
Number of pages	6
Journal	Journal of Siberian Federal University - Mathematics and Physics
Volume	8
Issue number	2
DOIs	https://doi.org/10.17516/1997-1397-2015-8-2-134-139
State	Published - 1 May 2015

Bibliographical note

Publisher Copyright:
© Siberian Federal University. All rights reserved.

Keywords

Lattice point
Logarithmic residue

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10.17516/1997-1397-2015-8-2-134-139

Cite this

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An integral formula for the number of lattice points in a domain

Abstract

Bibliographical note

Keywords

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