On a metrical theorem of W. Schmidt
On a series of cosecants related to a problem in ergodic theory
On a theorem of V. Bernik in the metric theory of Diophantine approximation
On infinite series representations of real numbers
On Kurzweil's 0-1 law in inhomogeneous Diophantine approximation
We give a necessary and sufficient condition such that, for almost all s ∈ ℝ, ||nθ - s|| < ψ(n) for infinitely many n ∈ ℕ, where θ is fixed and ψ(n) is a positive, non-increasing sequence. This can be seen as a dual result to classical theorems of Khintchine and Szüsz which dealt with the situation where s is fixed and θ is random. Moreover, our result contains several earlier ones as special cases: two old theorems of Kurzweil, a theorem of Tseng and a recent...
On metric Diophantine approximation in positive characteristic
On metric diophantine approximation of complex numbers, complex continued fractions
On metric theory of Diophantine approximation for complex numbers
In 1941, R. J. Duffin and A. C. Schaeffer conjectured that for the inequality |α - m/n| < ψ(n)/n with g.c.d.(m,n) = 1, there are infinitely many solutions in positive integers m and n for almost all α ∈ ℝ if and only if . As one of partial results, in 1978, J. D. Vaaler proved this conjecture under the additional condition . In this paper, we discuss the metric theory of Diophantine approximation over the imaginary quadratic field ℚ(√d) with a square-free integer d < 0, and show that a Vaaler...
On the ergodicity of the Weyl sums cocycle
On the metric theory of inhomogeneous diophantine approximations
On the theorem of Jarník and Besicovitch
Patterson measure and ubiquity.
Recouvrement d'un cercle par des intervalles
Regularity of distribution of (nα)-sequences
Répartition des suites et substitutions
Simultane diophantische Approximationen abhängiger Größen in mehreren Metriken
Simultaneous Diophantine approximation and asymptotic formulae on manifolds
Simultaneous inhomogeneous Diophantine approximation of the values of integral polynomials with respect to Archimedean and non-Archimedean valuations
We prove an analogue of the convergence part of Khintchine’s theorem for the simultaneous inhomogeneous Diophantine approximation on the Veronese curve with respect to the different valuations. It is an extension of the author’s earlier results.
Substitutions on two letters, cutting segments and their projections
In this paper we study the structure of the projections of the finite cutting segments corresponding to unimodular substitutions over a two-letter alphabet. We show that such a projection is a block of letters if and only if the substitution is Sturmian. Applying the procedure of projecting the cutting segments corresponding to a Christoffel substitution twice results in the original substitution. This induces a duality on the set of Christoffel substitutions.
Sur les approximations diophantiennes simultanées asymptotiques