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
On nodal sets and nodal domains on and
We discuss possible topological configurations of nodal sets, in particular the number of their components, for spherical harmonics on . We also construct a solution of the equation in that has only two nodal domains. This equation arises in the study of high energy eigenfunctions.
On Ramanujan's cubic continued fraction
On subsequences of convergents to a quadratic irrational given by some numerical schemes
Given a quadratic irrational , we are interested in how some numerical schemes applied to a convenient function provide subsequences of convergents to . We investigate three numerical schemes: secant-like methods and formal generalizations, which lead to linear recurring subsequences; the false position method, which leads to arithmetical subsequences of convergents and gives some interesting series expansions; Newton’s method, for which we complete a result of Edward Burger [1] about the existence...
On substitution invariant Sturmian words: an application of Rauzy fractals
Sturmian words are infinite words that have exactly n+1 factors of length n for every positive integer n. A Sturmian word sα,p is also defined as a coding over a two-letter alphabet of the orbit of point ρ under the action of the irrational rotation Rα : x → x + α (mod 1). A substitution fixes a Sturmian word if and only if it is invertible. The main object of the present paper is to investigate Rauzy fractals associated with two-letter invertible substitutions. As an application, we give...
On the average length of finite continued fractions
On the best rational approximations to transcendental numbers . II.
On the concept of optimality interval.
On the continued fractions of quadratic surds
On the Discrepancy of Convex Plane Sets.