Geodesic
On the integral criteria for a convergence of multidimensional Dirichlet series
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 11 (2014), pp. 76-86

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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, Newton polytope, toric variaty.
Mots-clés : quasi-elliptic polinomial 
@article{SEMR_2014_11_a76,
     author = {E. V. Zubchenkova},
     title = {On the integral criteria for a convergence of multidimensional {Dirichlet} series},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {76--86},
     publisher = {mathdoc},
     volume = {11},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2014_11_a76/}
}
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E. V. Zubchenkova. On the integral criteria for a convergence of multidimensional Dirichlet series. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 11 (2014), pp. 76-86. http://geodesic.mathdoc.fr/item/SEMR_2014_11_a76/