Roth's Theorem implies a Weakened Version of the ABC Conjecture for Special Cases
Autor: Philipp Sibbertsen and Karsten Müller and Timm Lampert and Michael Taktikos
Nummer: 700, Jul 2022, pp. 8
JEL-Class: C02; C60
Abstract:
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.
Zusammenfassung:
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