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Journal of Siberian Federal University. Mathematics & Physics, 2012, Volume 5, Issue 4, Pages 480–484
(Mi jsfu277)
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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
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
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
Linking options:
https://www.mathnet.ru/eng/jsfu277 https://www.mathnet.ru/eng/jsfu/v5/i4/p480
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Abstract page: | 316 | Full-text PDF : | 120 | References: | 43 |
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