Roth's theorem implies a weakened version of the ABC conjecture for special cases

Philipp Sibbertsen, Karsten Müller, Timm Lampert, Michael Taktikos

Enrico Bombieri proved that the ABC Conjecture implies Roth's theorem in 1994. This paper concerns the other direction. In making use of Bombieri's and Van der Poorten's explicit formula for the coefficients of the regular continued fractions of algebraic numbers, we prove that Roth's theorem implies a weakened non-effective version of the ABC Conjecture in certain cases relating to roots.

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Year of publication:	[2022]
Authors:	Sibbertsen, Philipp ; Müller, Karsten ; Lampert, Timm ; Taktikos, Michael
Publisher:	[Hannover] : [Wirtschaftswissenschaftliche Fakultät der Leibniz Universität Hannover]

Extent:	1 Online-Ressource (circa 8 Seiten)
Series:	Diskussionspapiere der Wirtschaftswissenschaftlichen Fakultät / Wirtschaftswissenschaftliche Fakultät, Universität Hannover : Hannover economic papers (HEP). - Hannover : Wirtschaftswiss. Fak., Univ., ZDB-ID 2120102-X. - Vol. [Nummer: 700 (Jul 2022)]
Type of publication:	Book / Working Paper
Type of publication (narrower categories):	Graue Literatur ; Non-commercial literature ; Arbeitspapier ; Working Paper
Language:	English
Other identifiers:	hdl:10419/268223 [Handle]
Classification:	C02 - Mathematical Methods ; C60 - Mathematical Methods and Programming. General
Source:	ECONIS - Online Catalogue of the ZBW

Persistent link: https://www.econbiz.de/10013414388