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arXiv · 1312.6767

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

Vefa Goksel·Shixiang Xia·Nigel Boston
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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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Vefa Goksel, Shixiang Xia, Nigel Boston. 2013-12-24. A Refined Conjecture For Factoring Iterates Of Quadratic Polynomials Over Finite Fields. https://arxiv.org/abs/1312.6767

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