Francesco Cellarosi

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We consider the ensemble of curves {γα,N : α ∈ (0, 1], N ∈ N} obtained by linearly interpolating the values of the normalized theta sum N− 1 2 ∑N ′−1 n=0 exp(πin α), 0 ≤ N ′ < N . We prove the existence of limiting finite-dimensional distributions for such curves as N →∞, with respect to an absolutely continuous probability measure μR on (0, 1]. Our Main(More)
A classical result of Khinchin says that for almost all real numbers α, the geometric mean of the first n digits ai(α) in the continued fraction expansion of α converges to a number K ≈ 2.6854520 . . . (Khinchin’s constant) as n → ∞. On the other hand, for almost all α, the arithmetic mean of the first n continued fraction digits ai(α) approaches infinity(More)
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