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              The aim of this thesis is to determine the natural boundary of meromorphy (when it exists) of an Euler product of n variables associated to a polynomial h \\in \\mathbf{Z } [X_1....,X_,n] satisfying an hypothesis of analytic regularity. Precisely it consists in finding the boundary of a maximal domain on which a meromorphic extension exists. We present in this thesis some methods which permit to extend in the multivariable case, under an hypothesis of analytic regularity which is mostly satisfied, the well-know result of Estermann concerning the maximal domain of meromorphy of an one variable Euler product \\prod_{p}h(p^{-s}) associated to a polynomial h with integral coefficients (such that Sh(0)=1S). We also precise the sense which we can give to the concept of "natural boundary" with regard to the real or complex dimension of a possible continuation beyond this boundary. As an application, we determine the natural boundary of a class of Euler products associated to a projective toric variety. A second application consists in the determination of the natural boundary of a class of Euler products of the form \\prod_{p}h(p^{-s_l },...,p^{-s_n},p^{-c }) where c is an integer (positive or negative). In particular we solve a problem of N. Kurokawa and H. Ochiai concerning the natural boundary of meromorphy of the multivariable lgusa zeta function Z^{\\textrm{ring} }(s_1,\\dots,s_n; \\mathbf{Z}[T,T^{-1}])
            """ ;
    dct:identifier "NNT: 2010STET4009" ;
    dct:issued "2026-05-25T13:41:42.915310"^^xsd:dateTime ;
    dct:language "fr" ;
    dct:modified "2026-05-25T13:41:42.915316"^^xsd:dateTime ;
    dct:publisher <https://rec.harvest-normandie.data4citizen.com/organization/cce9db95-46d9-4dc2-84b6-764215d0a002> ;
    dct:title "Maximal domain of meromorphy and natural boundary of uniform Euler products of one or several variables" ;
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    dcat:keyword "frontiere-naturelle",
        "infoeu-reposemanticsdoctoralthesis",
        "mathmath-gmmathematics-mathgeneral-mathematics-mathgm",
        "point-rationnel-sur-une-variete-torique",
        "polynome-cyclotomique",
        "produits-euleriens-multivariables",
        "prolongement-meromorphe",
        "theses" ;
    dcat:landingPage <https://theses.hal.science/tel-00677034> .

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    dct:issued "2026-05-25T13:41:43.014761"^^xsd:dateTime ;
    dct:modified "2026-05-25T13:41:42.893376"^^xsd:dateTime ;
    dct:title "Maximal domain of meromorphy and natural boundary of uniform Euler products of one or several variables" ;
    dcat:accessURL <https://theses.hal.science/tel-00677034> .

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