Comptes Rendus
no. 23-24
Complex Analysis/Number Theory
An abc theorem on the disk
[Un théorème du type abc sur le disque]

Présenté par : Gilles Pisier

Konstantin M. Dyakonov1
1 ICREA and Universitat de Barcelona, Departament de Matemàtica Aplicada i Anàlisi, Gran Via 585, 08007 Barcelona, Spain
Comptes Rendus. Mathématique, Volume 348 (2010) no. 23-24, pp. 1259-1261.

On généralise le « théorème abc » sur les polynômes (alias le théorème de Mason–Stothers) au cas des fonctions analytiques arbitraires sur le disque.

We extend the classical abc theorem for polynomials (also known as Mason's, or Mason–Stothers', theorem) to general analytic functions on the disk.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2010.10.030

Konstantin M. Dyakonov 1

1 ICREA and Universitat de Barcelona, Departament de Matemàtica Aplicada i Anàlisi, Gran Via 585, 08007 Barcelona, Spain 
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Konstantin M. Dyakonov. An abc theorem on the disk. Comptes Rendus. Mathématique, Volume 348 (2010) no. 23-24, pp. 1259-1261. doi : 10.1016/j.crma.2010.10.030. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.10.030/

[1] L. Carleson A representation formula for the Dirichlet integral, Math. Z., Volume 73 (1960), pp. 190-196

[2] K.M. Dyakonov Factorization of smooth analytic functions via Hilbert–Schmidt operators, St. Petersburg Math. J., Volume 8 (1997), pp. 543-569

[3] K.M. Dyakonov Local abc theorems for analytic functions | arXiv

[4] A. Granville; T.J. Tucker It's as easy as abc, Notices Amer. Math. Soc., Volume 49 (2002), pp. 1224-1231

[5] G.G. Gundersen; W.K. Hayman The strength of Cartan's version of Nevanlinna theory, Bull. London Math. Soc., Volume 36 (2004), pp. 433-454

[6] S. Lang Old and new conjectured Diophantine inequalities, Bull. Amer. Math. Soc. (N.S.), Volume 23 (1990), pp. 37-75

[7] T. Sheil-Small Complex Polynomials, Cambridge Studies in Advanced Mathematics, vol. 75, Cambridge University Press, Cambridge, 2002

[8] W.W. Stothers Polynomial identities and Hauptmoduln, Quart. J. Math. Oxford Ser. (2), Volume 32 (1981), pp. 349-370

[9] S.A. Vinogradov; N.A. Shirokov The factorization of analytic functions with derivative in Hp, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI), Volume 22 (1971), pp. 8-27 (in Russian)

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☆ Supported in part by grant MTM2008-05561-C02-01 from El Ministerio de Ciencia e Innovación (Spain) and grant 2009-SGR-1303 from AGAUR (Generalitat de Catalunya).

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