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

Multidimensional continued fractions generalize classical continued fractionswith the aim of providing periodic representations of algebraic irrationalitiesby means of integer sequences. However, there does not exist any algorithm thatprovides a periodic multidimensional continued fraction when algebraicirrationalities are given as inputs. In this paper, we provide acharacterization for periodicity of Jacobi--Perron algorithm by means of linearrecurrence sequences. In particular, we prove that partial quotients of amultidimensional continued fraction are periodic if and only if numerators anddenominators of convergents are linear recurrence sequences, generalizingsimilar results that hold for classical continued fractions.

Linear recurrence sequences and periodicity of multidimensional continued fractions