Displaying similar documents to “Ahlfors’ currents in higher dimension”

Extension of CR functions to «wedge type» domains

Andrea D'Agnolo, Piero D'Ancona, Giuseppe Zampieri (1991)

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

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Let X be a complex manifold, S a generic submanifold of X R , the real underlying manifold to X . Let Ω be an open subset of S with ∂ ⁡ Ω analytic, Y a complexification of S . We first recall the notion of Ω -tuboid of X and of Y and then give a relation between; we then give the corresponding result in terms of microfunctions at the boundary. We relate the regularity at the boundary for ∂ ¯ b to the extendability of C ⁢ R functions on Ω to Ω -tuboids of X . Next, if X has complex dimension 2, we give results...

The unit group of some fields of the form ℚ ( 2 , p , q , - l )

Moha Ben Taleb El Hamam (2024)

Mathematica Bohemica

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Let p and q be two different prime integers such that p ≡ q ≡ 3 ( mod 8 ) with ( p / q ) = 1 , and l a positive odd square-free integer relatively prime to p and q . In this paper we investigate the unit groups of number fields 𝕃 = ℚ ( 2 , p , q , - l ) .

A result on extension of C.R. functions

Makhlouf Derridj, John Erik Fornaess (1983)

Annales de l'institut Fourier

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Let Ω an open set in C 4 near z 0 ∈ ∂ Ω , λ a suitable holomorphic function near z 0 . If we know that we can solve the following problem (see [M. Derridj, Annali. Sci. Norm. Pisa, Série IV, vol. IX (1981)]) : ∂ ‾ u = λ f , ( f is a ( 0 , 1 ) form, ∂ ‾ closed in U ( z 0 ) in U ( z 0 ) with supp ( u ) ⊂ Ω ‾ ∩ U ( z 0 ) , then we deduce an extension result for C . R . functions on ∂ Ω ∩ U ( z 0 ) , as holomorphic fonctions in Ω ∩ V ( z 0 ) .

Uniqueness and factorization of Coleff-Herrera currents

Mats Andersson (2009)

Annales de la faculté des sciences de Toulouse Mathématiques

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We prove a uniqueness result for Coleff-Herrera currents which in particular means that if f = ( f 1 , ... , f m ) defines a complete intersection, then the classical Coleff-Herrera product associated to f is the unique Coleff-Herrera current that is cohomologous to 1 with respect to the operator δ f - ∂ ¯ , where δ f is interior multiplication with f . From the uniqueness result we deduce that any Coleff-Herrera current on a variety Z is a finite sum of products of residue currents with support on Z and holomorphic...

On analytic rapidly decreasing functions of a real variable

Gianfranco Cimmino (1983)

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

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Condizione necessaria e sufficiente affinché una funzione rapidamente decrescente di variabile reale sia uniformemente analitica è che per i suoi coefficienti γ 0 , γ 1 , … di Fourier-Hermite riesca γ m = 0 ⁢ ( e m ⁢ t ) per t > 0 abbastanza piccolo.

Biholomorphic maps determined on the boundary

Nozomu Mochizuki (1977)

Annales de l'institut Fourier

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Let D be a bounded domain in C n such that the boundary b D is topologically S 2 n - 1 in R 2 n with a regular point; let f : D ˜ → C n be a holomorphic map where D ˜ is a neighborhood of D ‾ . If f is one-to-one when restricted to b D , then f : D → f ( D ) is biholomorphic.

Bicyclotomic polynomials and impossible intersections

David Masser, Umberto Zannier (2013)

Journal de Théorie des Nombres de Bordeaux

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In a recent paper we proved that there are at most finitely many complex numbers t ≠ 0 , 1 such that the points ( 2 , 2 ( 2 - t ) ) and ( 3 , 6 ( 3 - t ) ) are both torsion on the Legendre elliptic curve defined by y 2 = x ( x - 1 ) ( x - t ) . In a sequel we gave a generalization to any two points with coordinates algebraic over the field Q ( t ) and even over C ( t ) . Here we reconsider the special case ( u , u ( u - 1 ) ( u - t ) ) and ( v , v ( v - 1 ) ( v - t ) ) with complex numbers u and v .