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

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Definable holomorphic continuations in o-minimal structures

By Adele Padgett

Appears in 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.

Information about the video

Date of recording 10/02/2025
Date of publication 28/02/2025
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.20304103
Cite this video 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

Domain(s)

Bibliography

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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