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Definable holomorphic continuations in o-minimal structures
Multi angle
Authors : Padgett, Adele (Author of the conference)
CIRM (Publisher )
03C40 - Interpolation, preservation, definability
03C64 - Model theory of ordered structures; o-minimality
32B20 - Semi-analytic sets and subanalytic sets, See also {14P15}
32D15 - Continuation of analytic objects
CIRM (Publisher )
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Abstract :
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.
Keywords : o-minimality; definability; analytic continuation; multisummable series; convergent generalized power series
MSC Codes : Keywords : o-minimality; definability; analytic continuation; multisummable series; convergent generalized power series
03C40 - Interpolation, preservation, definability
03C64 - Model theory of ordered structures; o-minimality
32B20 - Semi-analytic sets and subanalytic sets, See also {14P15}
32D15 - Continuation of analytic objects
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 28/02/2025 Conference Date : 10/02/2025 Subseries : Research talks arXiv category : Logic ; Complex Variables Mathematical Area(s) : Analysis and its Applications ; Logic and Foundations Format : MP4 (.mp4) - HD Video Time : 00:53:57 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2025-02-10_Padgett.mp4 
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Information on the Event
Event Title : Tame Geometry Thematic Month Week 3 / Géométrie modérée Mois thématique semaine 3Event Organizers : Matusinski, Mickael ; Rond, Guillaume ; Servi, Tamara ; Speissegger, Patrick Dates : 10/02/2025 - 14/02/2025 Event Year : 2025 Event URL : https://conferences.cirm-math.fr/3269.html
Citation Data
DOI : 10.24350/CIRM.V.20304103Cite this video as: Padgett, Adele (2025). Definable holomorphic continuations in o-minimal structures. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20304103 URI : http://dx.doi.org/10.24350/CIRM.V.20304103 |
See Also
- [Multi angle] Parametrizations in valued fields / Author of the conference Vermeulen, Floris.
- [Multi angle] Sharply o-minimal structures and sharp cell decomposition / Author of the conference Zak, Benny.
- [Multi angle] Hensel minimality / Author of the conference Rideau-Kikuchi, Silvain.
- [Multi angle] Tame geometry in quantum field theory and gravity / Author of the conference Grimm, Thomas.
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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