The existential closedness problem for analytic solutions of difference equations | Vidéo | Carmin.tv

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The existential closedness problem for analytic solutions of difference equations

By Adele Padgett

Appears in collection : Model theory of valued fields / Théorie des modèles des corps valués

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.

Information about the video

Date of recording 02/06/2023
Date of publication 23/06/2023
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Jean Petit
Format MP4

Citation data

DOI 10.24350/CIRM.V.20053103
Cite this video Padgett, Adele (02/06/2023). The existential closedness problem for analytic solutions of difference equations. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20053103
URL https://dx.doi.org/10.24350/CIRM.V.20053103

Domain(s)

Logic

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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