A metric theorem for restricted Diophantine approximation in positive characteristic
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
An application of metric diophantine approximation in hyperbolic space to quadratic forms.
For any real τ, a lim sup set WG,y(τ) of τ-(well)-approximable points is defined for discrete groups G acting on the Poincaré model of hyperbolic space. Here y is a 'distinguished point' on the sphere at infinity whose orbit under G corresponds to the rationals (which can be regarded as the orbit of the point at infinity under the modular group) in the classical theory of diophantine approximation.In this paper the Hausdorff dimension of the set WG,y(τ) is determined for geometrically finite groups...
An ergodic sum related to the approximation by continued fractions.
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.
Arithmetic functions on Beatty sequences
Asymptotic behavior of the number of solutions for non-Archimedean Diophantine approximations