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Singularité de séries de Dirichlet associées à des polynômes de plusieurs variables et applications en théorie analytique des nombres

Driss Essouabri (1997)

Annales de l'institut Fourier

Soit P [ X 1 , ... , X n ] un polynôme. On appelle série de Dirichlet associée à P la fonction : s Z ( P ; s ) = m * n P ( m ) - s ( s ) . Dans cet article nous étudions l’existence et les propriétés du prolongement méromorphe d’une telle série sous l’hypothèse qu’il existe B ] 0 , 1 [ tel que : i) P ( x ) + quand | | x | | + et x [ B , + [ n et ii) d ( Z ( P ) , [ B , + [ n ) > 0 Z ( P ) = { z n | P ( z ) = 0 } . Cette hypothèse est probablement optimale et en tout cas contient strictement toutes les classes de polynômes déjà traitées antérieurement. Sous cette hypothèse nos principaux résultats sont : l’existence du prolongement méromorphe au plan...

Solutions to a class of polynomially generalized Bers–Vekua equations using Clifford analysis

Min Ku, Uwe Kähler, Paula Cerejeiras (2012)

Archivum Mathematicum

In this paper a class of polynomially generalized Vekua–type equations and of polynomially generalized Bers–Vekua equations with variable coefficients defined in a domain of Euclidean space are discussed. Using the methods of Clifford analysis, first the Fischer–type decomposition theorems for null solutions to these equations are obtained. Then we give, under some conditions, the solutions to the polynomially generalized Bers–Vekua equation with variable coefficients. Finally, we present the structure...

Some applications of the trace condition for pluriharmonic functions in Cn.

Alessandro Perotti (2000)

Publicacions Matemàtiques

In this paper we investigate some applications of the trace condition for pluriharmonic functions on a smooth, bounded domain in Cn. This condition, related to the normal component on ∂D of the ∂-operator, permits us to study the Neumann problem for pluriharmonic functions and the ∂-problem for (0,1)-forms on D with solutions having assigned real part on the boundary.

Strict plurisubharmonicity of Bergman kernels on generalized annuli

Yanyan Wang (2014)

Annales Polonici Mathematici

Let A ζ = Ω - ρ ( ζ ) · Ω ¯ be a family of generalized annuli over a domain U. We show that the logarithm of the Bergman kernel K ζ ( z ) of A ζ is plurisubharmonic provided ρ ∈ PSH(U). It is remarkable that A ζ is non-pseudoconvex when the dimension of A ζ is larger than one. For standard annuli in ℂ, we obtain an interesting formula for ² l o g K ζ / ζ ζ ̅ , as well as its boundary behavior.

Su alcune formule integrali per le funzioni di più variabili complesse

Guido Lupacciolu (1981)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

General topological conditions are given for integration cycles of a certain class of integral formulas for holomorphic functions of several complex variables.

Subharmonicity properties of the Bergman kernel and some other functions associated to pseudoconvex domains

Bo Berndtsson (2006)

Annales de l’institut Fourier

Let D be a pseudoconvex domain in t k × z n and let φ be a plurisubharmonic function in D . For each t we consider the n -dimensional slice of D , D t = { z ; ( t , z ) D } , let φ t be the restriction of φ to D t and denote by K t ( z , ζ ) the Bergman kernel of D t with the weight function φ t . Generalizing a recent result of Maitani and Yamaguchi (corresponding to n = 1 and φ = 0 ) we prove that log K t ( z , z ) is a plurisubharmonic function in D . We also generalize an earlier results of Yamaguchi concerning the Robin function and discuss similar results in the setting...

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