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 effective counting and equidistribution results for latticepoints in families of domains in hyperbolic spaces, of any dimension and overany field. The domains we focus on are defined as product sets with respect tothe Iwasawa decomposition. Several classical Diophantine problems can bereduced to counting lattice points in such domains, including distribution ofshortest solution to the gcd equation, and angular distribution of primitivevectors in the plane. We give an explicit and effective solution to theseproblems, and extend them to imaginary quadratic number fields. Furtherapplications include counting lifts of closed horospheres to hyperbolicmanifolds and establishing an equidistribution property of integral solutionsto the Diophantine equation defined by a Lorentz form.

Horospherical coordinates of lattice points in hyperbolic space: effective counting and equidistribution