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

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

Metadaten
Author details:	Lev A. Aizenberg, Nikolai Nikolaevich Tarkhanov ORCiD GND
URN:	urn:nbn:de:kobv:517-opus-70453
ISSN:	2193-6943
Publication series (Volume number):	Preprints des Instituts für Mathematik der Universität Potsdam (3 (2014) 3)
Publisher:	Universitätsverlag Potsdam
Place of publishing:	Potsdam
Publication type:	Preprint
Language:	English
Year of first publication:	2014
Publication year:	2014
Publishing institution:	Universität Potsdam
Publishing institution:	Universitätsverlag Potsdam
Release date:	2014/05/12
Tag:	lattice point; logarithmic residue
Volume:	3
Issue:	3
Number of pages:	7
Organizational units:	Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
DDC classification:	5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
MSC classification:	34-XX ORDINARY DIFFERENTIAL EQUATIONS / 34Dxx Stability theory [See also 37C75, 93Dxx] / 34D15 Singular perturbations
	34-XX ORDINARY DIFFERENTIAL EQUATIONS / 34Exx Asymptotic theory / 34E20 Singular perturbations, turning point theory, WKB methods
Collection(s):	Universität Potsdam / Schriftenreihen / Preprints des Instituts für Mathematik der Universität Potsdam, ISSN 2193-6943 / 2014
Publishing method:	Universitätsverlag Potsdam
License (German):	Keine öffentliche Lizenz: Unter Urheberrechtsschutz