On a problem of Alfréd Rényi
On a quantitative refinement of the Lagrange spectrum
On a theorem of Legendre in the theory of continued fractions
On a theorem of Segre
On an extension of Euler numbers and records of alternating permutations. (Sur une extension des nombres d'Euler et les records des permutations alternantes.)
On approximation by Lüroth series
Let and be its sequence of Lüroth Series convergents. Define the approximation coefficients by . In [BBDK] the limiting distribution of the sequence was obtained for a.e. using the natural extension of the ergodic system underlying the Lüroth Series expansion. Here we show that this can be done without the natural extension. In fact we will prove that for each is already distributed according to the limiting distribution. Using the natural extension we will study the distribution for...
On arithmetic properties of the convergents of Euler's number
On Best Two-Dimensional Dirichlet-Approximations and their Algorithmic Calculation.
On continued fractions and diophantine approximation in power series fields
On Continued Fractions and Finite Automata.
On Dispersion and Markov Constants.
On Ergodic Theory of A. Schmidt's Complex Continued Fractions over Gaussian Field.
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 Legendre's theorem related to diophantine approximations
On metric diophantine approximation of complex numbers, complex continued fractions
On metrical theory of diophantine approximation over imaginary quadratic field