A refined conjecture for factorizations of iterates of quadratic polynomials over finite fields

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

5 Scopus Citations
View graph of relations

Author(s)

Detail(s)

Original languageEnglish
Pages (from-to)304-311
Journal / PublicationExperimental Mathematics
Volume24
Issue number3
Publication statusPublished - 3 Jul 2015
Externally publishedYes

Abstract

Jones and Boston conjectured that the factorization process for iterates of irreducible quadratic polynomials over finite fields is approximated by a one-step Markov model. In this paper, we find unexpected and intricate behavior for some quadratic polynomials, in particular for those whose critical orbits have large cycle and small tail. We also propose a multistep Markov model that explains these new observations better than the model of Jones and Boston. © 2014 Taylor and Francis Group, LLC.

Research Area(s)

  • factorization, Iteration, Markov process, quadratic polynomial

Bibliographic Note

Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to lbscholars@cityu.edu.hk.