Francesco Cellarosi

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We consider the ensemble of curves {γ α,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 2 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 µ R on (0, 1]. Our Main(More)
We prove the existence of the limiting distribution for the sequence of denominators generated by continued fraction expansions with even partial quotients, which were introduced by F. Schweiger [14] [15] and studied also by C. Kraaikamp and A. Lopes [10]. Our main result is proven following the strategy used by Ya. Sinai and C. Ulcigrai [18] in their proof(More)
A classical result of Khinchin says that for almost all real numbers α, the geometric mean of the first n digits a i (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 a i (α) approaches infinity(More)
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