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Journal of Siberian Federal University. Mathematics & Physics, 2012, Volume 5, Issue 4, Pages 480–484 (Mi jsfu277)  

This article is cited in 1 scientific paper (total in 1 paper)

A multidimensional analog of the Weierstrass $\zeta$-function in the problem of the number of integer points in a domain

Elena N. Tereshonok, Alexey V. Shchuplev

Institute of Mathematics, Siberian Federal University, Krasnoyarsk, Russia
Full-text PDF (139 kB) Citations (1)
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Abstract: A multidimensional analog of the Weierstrass $\zeta$-function in $\mathbb C^n$ is a differential $(0,n-1)$-form with singularities in the points of the integer lattice $\Gamma\subset\mathbb C^n$. Using this form we construct a $\Gamma$-invariant $(n,n-1)$-form $\tau(z)\wedge dz$. The integral of this form over a domain's boundary is equal to difference between the number of integer points in the domain and its volume.
Keywords: Weierstrass $\zeta$-function, integer lattice, Bochner–Martinelli kernel, Gauss circle problem.
Received: 21.03.2012
Received in revised form: 21.04.2012
Accepted: 15.05.2012
Document Type: Article
UDC: 517.55
Language: English
Citation: Elena N. Tereshonok, Alexey V. Shchuplev, “A multidimensional analog of the Weierstrass $\zeta$-function in the problem of the number of integer points in a domain”, J. Sib. Fed. Univ. Math. Phys., 5:4 (2012), 480–484
Citation in format AMSBIB
\Bibitem{TerSch12}
\by Elena~N.~Tereshonok, Alexey~V.~Shchuplev
\paper A multidimensional analog of the Weierstrass $\zeta$-function in the problem of the number of integer points in a~domain
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2012
\vol 5
\issue 4
\pages 480--484
\mathnet{http://mi.mathnet.ru/jsfu277}
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  • https://www.mathnet.ru/eng/jsfu/v5/i4/p480
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Журнал Сибирского федерального университета. Серия "Математика и физика"
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    Full-text PDF :120
    References:43
     
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