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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)

- Francesco Cellarosi, Doug Hensley, Steven J. Miller, Jake L. Wellens
- Experimental Mathematics
- 2015

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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