Mathematics > Number Theory
[Submitted on 21 Dec 2018 (v1), last revised 20 May 2019 (this version, v2)]
Title:Continued Fractions of Arithmetic Sequences of Quadratics
View PDFAbstract:Let x be a quadratic irrational and let P be the set of prime numbers. We show the existence of an infinite subset S of P such that the statistics of the period of the continued fraction expansions along the sequence {px: p\in S} approach the normal statistics given by the Gauss-Kuzmin measure. Under the generalized Riemann hypothesis, we prove that there exist full density subsets S of P and T of N satisfying the same assertion. We give a rate of convergence in all cases.
Submission history
From: Menny Aka [view email][v1] Fri, 21 Dec 2018 14:52:35 UTC (12 KB)
[v2] Mon, 20 May 2019 09:16:52 UTC (12 KB)
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