3 papers
math.NT2026
From ABC to Effective Roth and Ridout Constants for Cubic Roots
Karsten Müller, Michael Taktikos
Enrico Bombieri showed conditionally (1994) that the ABC conjecture implies Roth's theorem, and Van Frankenhuysen (1999) later provided a complete proof. Building on Bombieri's and…
math.NT2022
Do algebraic numbers follow Khinchin's Law?
Philipp Sibbertsen, Timm Lampert, Karsten Müller +1
The coefficients of the regular continued fraction for random numbers are distributed by the Gauss-Kuzmin distribution according to Khinchin's law. Their geometric mean converges t…
math.NT2022
Roth's Theorem implies a Weakened Version of the ABC Conjecture for Special Cases
Philipp Sibbertsen, Timm Lampert, Karsten Müller +1
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 f…