Continued Fractions of Arithmetic Sequences of Quadratics

2018/12/21 by Aka, Menny
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1812.09163

Abstract

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∈ 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.

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