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pro vyhledávání: '"Taktikos, Michael"'
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 to Khinchin's constant and their rational approximation speed is Khinch
Externí odkaz:
http://arxiv.org/abs/2208.14359
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 alge
Externí odkaz:
http://arxiv.org/abs/2208.14354
This paper argues that the distribution of the coefficients of the regular continued fraction should be considered for each algebraic number of degree >2 separately. For random numbers the coefficients are distributed by the Gauss-Kuzmin distribution
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=od______1687::8a0b1ad692f26db03660de5244b600b5
https://hdl.handle.net/10419/235234
https://hdl.handle.net/10419/235234