Algebraic Computations with Continued Fractions

Ergodic Computations with Continued Fractions and Jacobi ' s Algorithm

Ergodic computational aspects of the Jacobi algorithm, a generalization to two dimensions of the continued fraction algorithm, are considered. By means of such computations the entropy of the algorithm is estimated to be 3.5. An approximation to the, invariant measure of the transformation associated with the algorithm is obtained. The computations are tested by application to the continued fra...

Algebraic continued fractions in F q ( ( T −

On the complexity of algebraic numbers, II. Continued fractions

Let b 2 be an integer. Émile Borel [9] conjectured that every real irrational algebraic number α should satisfy some of the laws shared by almost all real numbers with respect to their b-adic expansions. Despite some recent progress [1], [3], [7], we are still very far away from establishing such a strong result. In the present work, we are concerned with a similar question, where the b-adic ex...

Continued Fractions with Multiple Limits

For integers m ≥ 2, we study divergent continued fractions whose numerators and denominators in each of the m arithmetic progressions modulo m converge. Special cases give, among other things, an infinite sequence of divergence theorems, the first of which is the classical Stern-Stolz theorem. We give a theorem on a class of Poincaré type recurrences which shows that they tend to limits when th...

Transcendence with Rosen Continued Fractions

We give the first transcendence results for the Rosen continued fractions. Introduced over half a century ago, these fractions expand real numbers in terms of certain algebraic numbers.