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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2014, Volume 11, Pages 76–86
(Mi semr473)
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This article is cited in 1 scientific paper (total in 1 paper)
Real, complex and functional analysis
On the integral criteria for a convergence of multidimensional Dirichlet series
E. V. Zubchenkova Siberian Federal University, Krasnoyarsk
Abstract:
We consider Dirichlet series associated with a set of $m$ polynomials in $n$ variables. Such series depend on $m$ complex parameters. They were studed by B. Lichtin and others in the case of hypoelliptic polynomials. We consider a more general class of polynomials so called quasielliptic polynomials in the sence of T. Ermolaeva and A. Tsikh. Using the toric geometry we discribe the domain of convergence in terms of Newton polytopes of polynomials defining the series. As an auxiliary statement we give a criterion for convergence of some integrals over $\mathbb {R}^n$.
Keywords:
multidimensional Dirichlet series, quasi-elliptic polinomial, Newton polytope, toric variaty.
Received January 11, 2014, published February 5, 2014
Citation:
E. V. Zubchenkova, “On the integral criteria for a convergence of multidimensional Dirichlet series”, Sib. Èlektron. Mat. Izv., 11 (2014), 76–86
Linking options:
https://www.mathnet.ru/eng/semr473 https://www.mathnet.ru/eng/semr/v11/p76
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