Definable holomorphic continuations in o-minimal structures | Vidéo | Carmin.tv

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Definable holomorphic continuations in o-minimal structures

De Adele Padgett

Apparaît dans la collection : Tame Geometry Thematic Month Week 3 / Géométrie modérée Mois thématique semaine 3

A real analytic function can always be continued holomorphically to some domain. However, the holomorphic continuations of definable functions in an o-minimal structure may not be definable. I will present joint work with P. Speissegger in which we study holomorphic continuations of functions definable in two o-minimal expansions of the real field. I will also discuss how to apply these results to the complex Gamma function and Riemann zeta function.

Informations sur la vidéo

Date de captation 10/02/2025
Date de publication 28/02/2025
Institut CIRM
Licence CC BY NC ND
Langue Anglais
Audience Chercheurs, Doctorants
Réalisateur(s) Guillaume Hennenfent
Format MP4

Données de citation

DOI 10.24350/CIRM.V.20304103
Citer cette vidéo Padgett, Adele (10/02/2025). Definable holomorphic continuations in o-minimal structures. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20304103
URL https://dx.doi.org/10.24350/CIRM.V.20304103

Domaine(s)

Bibliographie

BIANCONI, Ricardo. Nondefinability results for expansions of the field of real numbers by the exponential function and by the restricted sine function. The Journal of Symbolic Logic, 1997, vol. 62, no 4, p. 1173-1178. - http://doi.org/10.2307/2275634
T. Kaiser. Global complexification of real analytic globally subanalytic functions. Israel J. Math., 213(1):139–173, 2016 - https://doi.org/10.1007/s11856-016-1306-9
KAISER, Tobias et SPEISSEGGER, Patrick. Analytic continuations of log-exp-analytic germs. Transactions of the American Mathematical Society, 2019, vol. 371, no 7, p. 5203-5246. - https://doi.org/10.1090/tran/7748
WILKIE, Alex J. Complex continuations of ℝan, exp-definable unary functions with a diophantine application. Journal of the London Mathematical Society, 2016, vol. 93, no 3, p. 547-566. - https://doi.org/10.1112/jlms/jdw007

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