A note on simultaneous Diophantine approximation in positive characteristic
A note on the Hausdorff-Besicovitch dimension of systems of linear forms
A note on the weighted Khintchine-Groshev Theorem
Let denote the set of –approximable points in . The classical Khintchine–Groshev theorem assumes a monotonicity condition on the approximating functions . Removing monotonicity from the Khintchine–Groshev theorem is attributed to different authors for different cases of and . It can not be removed for as Duffin–Schaeffer provided the counter example. We deal with the only remaining case and thereby remove all unnecessary conditions from the Khintchine–Groshev theorem.
A note on zero-one laws in metrical Diophantine approximation
A problem of Erdős-Szüsz-Turán on diophantine approximation
Algebraic integers near the unit circle
All Liouville Numbers are Transcendental
In this Mizar article, we complete the formalization of one of the items from Abad and Abad’s challenge list of “Top 100 Theorems” about Liouville numbers and the existence of transcendental numbers. It is item #18 from the “Formalizing 100 Theorems” list maintained by Freek Wiedijk at http://www.cs.ru.nl/F.Wiedijk/100/. Liouville numbers were introduced by Joseph Liouville in 1844 [15] as an example of an object which can be approximated “quite closely” by a sequence of rational numbers. A real...
An equivalent of Kronecker's theorem for powers of an algebraic number and structure of linear recurrences of fixed length
An extension of a theorem of Duffin and Schaeffer in Diophantine approximation
Duffin and Schaeffer have generalized the classical theorem of Khintchine in metric Diophantine approximation in the case of any error function under the assumption that all the rational approximants are irreducible. This result is extended to the case where the numerators and the denominators of the rational approximants are related by a congruential constraint stronger than coprimality.
An extension of the Khinchin-Groshev theorem
We prove a version of the Khinchin-Groshev theorem in Diophantine approximation for quadratic extensions of function fields in positive characteristic.
Approximations diophantiennes asymptotiques.
Approximations diophantiennes dans un corps local
Approximations diophantiennes et eutaxie
Asymptotic behavior of the number of solutions for non-Archimedean Diophantine approximations
Complex dimensions of self-similar fractal strings and Diophantine approximation.
Continued fractions, multidimensional diophantine approximations and applications
This paper is a brief review of some general Diophantine results, best approximations and their applications to the theory of uniform distribution.
Counting rational points near planar curves
We find an asymptotic formula for the number of rational points near planar curves. More precisely, if f:ℝ → ℝ is a sufficiently smooth function defined on the interval [η,ξ], then the number of rational points with denominator no larger than Q that lie within a δ-neighborhood of the graph of f is shown to be asymptotically equivalent to (ξ-η)δQ².
Diophantine approximation, Hausdorff dimension and Schroder's functional equation
Diophantine approximation on affine hyperplanes
Entropies of the partitions of the unit interval generated by the Farey tree