A Refined Conjecture For Factoring Iterates Of Quadratic Polynomials Over Finite Fields

2013/12/24 by Vefa Goksel, Goksel, Vefa, Shixiang Xia +3
Mathematics · #37P25 #60J20 #FOS: Mathematics #Number Theory (math.NT) #Primary 11T55 #math.NT #msc:11T55 #msc:37P25 #msc:60J20

paper · pdf · doi:10.48550/arxiv.1312.6767

13 pages

arxiv created 2013/12/25 · arxiv updated 2013/12/30

Abstract

Jones and Boston conjectured that the factorization process for iterates of irreducible quadratic polynomials over finite fields is approximated by a Markov model. In this paper, we find unexpected and intricate behavior for some quadratic polynomials, in particular for the ones with tail size one. We also propose a multi-step Markov model that explains these new observations better than the model of Jones and Boston.

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