On a measure theoretic aspect of diophantine approximation.
On a metrical theorem of W. Schmidt
On a theorem of V. Bernik in the metric theory of Diophantine approximation
On approximation of real numbers by real algebraic numbers
On Baker type lower bounds for linear forms
A criterion is given for studying (explicit) Baker type lower bounds of linear forms in numbers over the ring of an imaginary quadratic field . This work deals with the simultaneous auxiliary functions case.
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 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 simultaneous inhomogeneous Diophantine approximation
On the metric theory of inhomogeneous diophantine approximations