English
On some diophantine equations in separated variables
Virtualconference
Auteurs : Bérczes, Attila (Auteur de la conférence)
CIRM (Editeur )
11C08 - Polynomials, See also {13F20}
11D41 - "Higher degree equations; Fermat's equation"
CIRM (Editeur )
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Résumé :
A Diophantine equation has separated variables if it is of the form $ f(x) = g(y)$ for polynomials $f$, $g$. In a more general sense the degree of $f $ and $g$ may also be a variable.In the present talk various results for special types of the polynomials $f$ and $g$ will be presented. The types of the considered polynomials contain power sums, sums of products of consecutive integers, Komornik polynomials, perfect powers. Results on $F$-Diophantine sets, which are proved using results on Diophantine equations in separated variables will also be considered. The main tool for the proof of the presented general qualitative results is the famous Bilu-Tichy Theorem. Further, effective results (which depend on Baker's method) and results containing the complete solutions to special cases of these equations will also be included.
Mots-Clés : Diophantine equation; separated variable; polynomials
Codes MSC : Mots-Clés : Diophantine equation; separated variable; polynomials
11C08 - Polynomials, See also {13F20}
11D41 - "Higher degree equations; Fermat's equation"
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de Publication : 01/12/2020 Date de Captation : 25/11/2020 Sous Collection : Research talks Catégorie arXiv : Number Theory Domaine(s) : Théorie des Nombres Format : MP4 (.mp4) - HD Durée : 00:46:39 Audience : Chercheurs Download : https://videos.cirm-math.fr/2020-11-25_Berczes.mp4 
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Informations sur la Rencontre
Nom de la Rencontre : Jean-Morlet Chair 2020 - Conference: Diophantine Problems, Determinism and Randomness / Chaire Jean-Morlet 2020 - Conférence : Problèmes diophantiens, déterminisme et aléatoireOrganisateurs de la Rencontre : Rivat, Joël ; Tichy, Robert Dates : 23/11/2020 - 27/11/2020 Année de la rencontre : 2020 URL de la Rencontre : https://www.chairejeanmorlet.com/2256.html
Données de citation
DOI : 10.24350/CIRM.V.19685903Citer cette vidéo: Bérczes, Attila (2020). On some diophantine equations in separated variables. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19685903 URI : http://dx.doi.org/10.24350/CIRM.V.19685903 |
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