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The existential closedness problem for analytic solutions of difference equations
Multi angle
Authors : ... (Author of the conference)
... (Publisher )
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
... (Publisher )
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Abstract :
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.
Keywords : existential closedness; $\Gamma $-function
MSC Codes : Keywords : 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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Information on the Video
Language : EnglishAvailable date : 23/06/2023 Conference Date : 02/06/2023 Subseries : Research talks arXiv category : Logic Mathematical Area(s) : Algebraic & Complex Geometry ; Logic and Foundations Format : MP4 (.mp4) - HD Video Time : 01:00:14 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2023_06-02_Padgett_1.mp4 
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Information on the Event
Event Title : Model theory of valued fields / Théorie des modèles des corps valuésDates : 29/05/2023 - 02/06/2023 Event Year : 2023 Event URL : https://conferences.cirm-math.fr/2761.html
Citation Data
DOI : 10.24350/CIRM.V.20053103Cite this video as: (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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Bibliography
- 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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