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/

Zendy Open

Presents the pdf analysis as premium feature

PDF Analysis

Insights

Presents the summarisation as premium feature

Summarisation

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Letdenote the set of ψ-approximable points in. Under the assumption that the approximating function ψ is monotonic, the classical Khintchine–Groshev theorem provides an elegant probabilistic criterion for the Lebesgue measure of. The famous Duffin–Schaeffer counterexample shows that the monotonicity assumption on ψ is absolutely necessary when  m  =  n  = 1. On the other hand, it is known that monotonicity is not necessary when  n  ≥ 3 (Schmidt) or when  n  = 1 and  m  ≥ 2 (Gallagher). Surprisingly, when  n  = 2, the situation is unresolved. We deal with this remaining case and thereby remove all unnecessary conditions from the classical Khintchine–Groshev theorem. This settles a multidimensional analog of Catlin's conjecture.

Classical Metric Diophantine Approximation Revisited: The Khintchine–Groshev Theorem