English
The existential closedness problem for analytic solutions of difference equations
Multi angle
Auteurs : Padgett, Adele (Auteur de la conférence)
CIRM (Editeur )
03C05 - Equational classes, universal algebra, See also {08Axx}
11U09 - Model theory, See also {03Cxx}
30C15 - "Zeros of polynomials, rational functions, and other analytic functions (e.g. zeros of functions with bounded Dirichlet integral), {For algebraic theory, See 12D10; for real methods, See 26C10}"
32A60 - Zero sets of holomorphic functions
33B15 - Gamma, beta and polygamma functions
CIRM (Editeur )
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Résumé :
The existential closedness problem for a function $f$ is to show that a system of complex polynomials in $2 n$ variables always has solutions in the graph of $f$, except when there is some geometric obstruction. Special cases have be proven for exp, Weierstrass $\wp$ functions, the Klein $j$ function, and other important functions in arithmetic geometry using a variety of techniques. Recently, some special cases have also been studied for well-known solutions of difference equations using different methods. There is potential to expand on these results by adapting the strategies used to prove existential closedness results for functions in arithmetic geometry to work for analytic solutions of difference equations.
Mots-Clés : existential closedness; $\Gamma $-function
Codes MSC : Mots-Clés : existential closedness; $\Gamma $-function
03C05 - Equational classes, universal algebra, See also {08Axx}
11U09 - Model theory, See also {03Cxx}
30C15 - "Zeros of polynomials, rational functions, and other analytic functions (e.g. zeros of functions with bounded Dirichlet integral), {For algebraic theory, See 12D10; for real methods, See 26C10}"
32A60 - Zero sets of holomorphic functions
33B15 - Gamma, beta and polygamma functions
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Informations sur la Vidéo
Réalisateur : Petit, JeanLangue : Anglais Date de Publication : 23/06/2023 Date de Captation : 02/06/2023 Sous Collection : Research talks Catégorie arXiv : Logic Domaine(s) : Géométrie Complexe & géométrie Algébrique ; Logique et Fondements Format : MP4 (.mp4) - HD Durée : 01:00:14 Audience : Chercheurs ; Etudiants Science Cycle 2 ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2023_06-02_Padgett_1.mp4 
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Informations sur la Rencontre
Nom de la Rencontre : Model theory of valued fields / Théorie des modèles des corps valuésOrganisateurs de la Rencontre : Chatzidakis, Zoé ; Jahnke, Franziska ; Rideau-Kikuchi, Silvain Dates : 29/05/2023 - 02/06/2023 Année de la rencontre : 2023 URL de la Rencontre : https://conferences.cirm-math.fr/2761.html
Données de citation
DOI : 10.24350/CIRM.V.20053103Citer cette vidéo: Padgett, Adele (2023). The existential closedness problem for analytic solutions of difference equations. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20053103 URI : http://dx.doi.org/10.24350/CIRM.V.20053103 |
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Bibliographie
- ASLANYAN, Vahagn, KIRBY, Jonathan, et MANTOVA, Vincenzo. A geometric approach to some systems of exponential equations. International Mathematics Research Notices, 2023, vol. 2023, no 5, p. 4046-4081. - https://doi.org/10.1093/imrn/rnab340
- ETEROVIĆ, Sebastian et HERRERO, Sebastián. Solutions of equations involving the modular 𝑗 function. Transactions of the American Mathematical Society, 2021, vol. 374, no 6, p. 3971-3998. - http://dx.doi.org/10.1090/tran/8244
- LI, Bao Qin et STEUDING, Jörn. Fixed points of the Riemann zeta function and dirichlet series. Monatshefte für Mathematik, 2022, vol. 198, no 3, p. 581-589. - http://dx.doi.org/10.1007/s00605-022-01709-x
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