Generalization of a theorem of Gauss-Kuzmin.
Hausdorff dimension of real numbers with bounded digit averages
How many points contain arithmetic progressions in their continued fraction expansion?
Irrational numbers of constant type -- a new characterization.
Khinchin type condition for translation surfaces and asymptotic laws for the Teichmüller flow
We study a diophantine property for translation surfaces, defined in terms of saddle connections and inspired by classical Khinchin condition. We prove that the same dichotomy holds as in Khinchin theorem, then we deduce a sharp estimate on how fast the typical Teichmüller geodesic wanders towards infinity in the moduli space of translation surfaces. Finally we prove some stronger result in genus one.
Khintchine types of translated coordinate hyperplanes
There has been great interest in developing a theory of "Khintchine types" for manifolds embedded in Euclidean space, and considerable progress has been made for curved manifolds. We treat the case of translates of coordinate hyperplanes, decidedly flat manifolds. In our main results, we fix the value of one coordinate in Euclidean space and describe the set of points in the fiber over that fixed coordinate that are rationally approximable at a given rate. We identify translated coordinate hyperplanes...
Limit Theorems for Sums of Partial Quotients of Continued Fractions.
Limiting curlicue measures for theta sums
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=0N'−1exp(πin2α), 0≤N'<N. We prove the existence of limiting finite-dimensional distributions for such curves as N→∞, when α is distributed according to any probability measure λ, absolutely continuous w.r.t. the Lebesgue measure on [0, 1]. Our Main Theorem generalizes a result by Marklof [Duke Math. J.97 (1999) 127–153] and Jurkat and van Horne [Duke...
Maximal -expansions are Bernoulli shifts
Metric and arithmetic properties of mediant-Rosen maps
Metric diophantine approximation and probability.
Metrische Kettenbruchprobleme
Mischungseigenschaften und Entropie beim Jacobischen Algorithmus.
Multi-continued fraction algorithm on multi-formal Laurent series
Natural numbers n for which ⌊nα + s⌋ ≠ ⌊nβ + s⌋
Non-normality of continued fraction partial quotients modulo q
On certain statistical properties of continued fractions with even and with odd partial quotients
On decimal and continued fraction expansions of a real number
On Legendre's theorem related to diophantine approximations
On metric diophantine approximation and subsequence ergodic theory.