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

Access to Document

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

Cite this

@article{cc3a6a2fdf9742abb9a91a8b07a30cd0,

title = "An integral formula for the number of lattice points in a domain",

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.",

keywords = "Lattice point, Logarithmic residue",

author = "Lev Aizenberg and Nikolai Tarkhanov",

year = "2015",

month = may,

day = "1",

doi = "10.17516/1997-1397-2015-8-2-134-139",

language = "אנגלית",

volume = "8",

pages = "134--139",

journal = "Journal of Siberian Federal University - Mathematics and Physics",

issn = "1997-1397",

publisher = "Siberian Federal University",

number = "2",

}

TY - JOUR

T1 - An integral formula for the number of lattice points in a domain

AU - Aizenberg, Lev

AU - Tarkhanov, Nikolai

PY - 2015/5/1

Y1 - 2015/5/1

N2 - 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.

AB - 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.

KW - Lattice point

KW - Logarithmic residue

UR - http://www.scopus.com/inward/record.url?scp=84930060309&partnerID=8YFLogxK

U2 - 10.17516/1997-1397-2015-8-2-134-139

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

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:84930060309

SN - 1997-1397

VL - 8

SP - 134

EP - 139

JO - Journal of Siberian Federal University - Mathematics and Physics

JF - Journal of Siberian Federal University - Mathematics and Physics

IS - 2

ER -

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

Abstract

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Cite this