English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We extend two results about the ordinary continued fraction expansion to bestsimultaneous Diophantine approximations of vectors or matrices. The first isLevy-Khintchin Theorem about the almost sure growth rate of the denominators ofthe convergents. The second is a Theorem of Bosma, Hendrik and Wiedijk aboutthe almost sure limit distribution of the sequence of products $q_nd(q_n\theta, Z)$ where the $q_n$'s are the denominators of the convergentsassociated with the real number $\theta$ by the ordinary continued fractionalgorithm. Beside these two main results, we show that when $d\ge2$, for almostall vectors $\theta\in R^d$, $\liminf_{n\to\infty} q_{n+k}d(q_n\theta, Z^d)=0$for all positive integers $k$, where $(q_n)_{n\in N}$ is the sequence of bestapproximation denominators of $\theta$.

Levy-Khintchin Theorem for best simultaneous Diophantine approximations