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Journal of Siberian Federal University. Mathematics & Physics, 2015, Volume 8, Issue 2, Pages 134–139
(Mi jsfu414)
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An integral formula for the number of lattice points in a domain
Lev Aizenberga, Nikolai Tarkhanovb
a Department of Mathematics, Bar-Ilan University, 52900 Ramat-Gan,
Israel
b Institute of Mathematics, University of Potsdam, Am Neuen Palais, 10, Potsdam, 14469, Germany
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 $\mathbb{R}^n$ and the volume of this domain. The difference proves to be the integral of an explicit differential form over the boundary of the domain.
Keywords:
logarithmic residue, lattice point.
Received: 06.02.2015
Received in revised form: 06.03.2015
Accepted: 14.04.2015
Citation:
Lev Aizenberg, Nikolai Tarkhanov, “An integral formula for the number of lattice points in a domain”, J. Sib. Fed. Univ. Math. Phys., 8:2 (2015), 134–139
Linking options:
https://www.mathnet.ru/eng/jsfu414 https://www.mathnet.ru/eng/jsfu/v8/i2/p134
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| Abstract page: | 307 | | Full-text PDF : | 127 | | References: | 53 |
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