On Hirzebruch sums and a theorem of Schinzel
On Hurwitzian and Tasoev's continued fractions
On inhomogeneous Diophantine approximation and the Nishioka-Shiokawa-Tamura algorithm
We obtain the values concerning using the algorithm by Nishioka, Shiokawa and Tamura. In application, we give the values (θ,1/2), (θ,1/a), (θ,1/√(ab(ab+4))) and so on when θ = (√(ab(ab+4)) - ab)/(2a) = [0;a,b,a,b,...].
On inhomogeneous diophantine approximation with some quasi-periodic expressions, II
We consider the values concerningwhere the continued fraction expansion of has a quasi-periodic form. In particular, we treat the cases so that each quasi-periodic form includes no constant. Furthermore, we give some general conditions satisfying .
On integers generated by a finite number of fixed primes
On irrationality measures of the values of Gauss hypergeometric function.
On irrationality of the values of certain series
On irregularities of distribution, III
On irregularities of distribution, IV
On Kronecker's limit formula for Dirichlet series with periodic coefficients
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 Legendre's theorem related to diophantine approximations
On limit points of subsequences of uniformly distributed sequences
Given a subsequence of a uniformly distributed sequence, relations between the asymptotic densities of sets of its indices and the Lebesgue measure of the set of all its limit points are studied.
On linear forms in the logarithms of algebraic numbers
On linear forms of a certain class of G-functions and p-adic G-functions
On linear forms of G-functions
On Lower Bounds for Polynomials in the Values of E-Functions.
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...