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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…