Jean-Morlet Chair 2020 - Conference: Diophantine Problems, Determinism and Randomness / Chaire Jean-Morlet 2020 - Conférence : Problèmes diophantiens, déterminisme et aléatoire

Collection Jean-Morlet Chair 2020 - Conference: Diophantine Problems, Determinism and Randomness / Chaire Jean-Morlet 2020 - Conférence : Problèmes diophantiens, déterminisme et aléatoire

Organizer(s) Rivat, Joël ; Tichy, Robert

Date(s) 23/11/2020 - 27/11/2020

linked URL https://www.chairejeanmorlet.com/2256.html

00:00:00 / 00:00:00

24 28

On some diophantine equations in separated variables

By Attila Bérczes

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.

Information about the video

Date of recording 25/11/2020
Date of publication 01/12/2020
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19685903
Cite this video Bérczes, Attila (25/11/2020). On some diophantine equations in separated variables. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19685903
URL https://dx.doi.org/10.24350/CIRM.V.19685903

Domain(s)

Number Theory

MSC codes

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