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 establish an equidistribution result for pushforwards of certain locally finite algebraic measures in the adelic extension of the space of lattices in the plane. As an application of our analysis, we obtain new results regarding the asymptotic normality of the continued fraction expansions of most rationals with a high denominator as well as an estimate on the length of their continued fraction expansions.  By similar methods, we also establish a complementary result to Zaremba's conjecture. Namely, we show that given a bound   M  , for any large   q  , the number of rationals    p  /  q  ∈  [  0  ,  1  ]    for which the coefficients of the continued fraction expansion of    p  /  q    are bounded by   M   is    o  (   q   1  −  ε    )    for some    ε  >  0   , which depends on   M  .

Equidistribution of divergent orbits and continued fraction expansion of rationals