# The Cycle Structure of Unicritical Polynomials

@article{Bridy2018TheCS, title={The Cycle Structure of Unicritical Polynomials}, author={Andrew Bridy and Derek Garton}, journal={International Mathematics Research Notices}, year={2018} }

A polynomial with integer coefficients yields a family of dynamical systems indexed by primes as follows: for any prime $p$, reduce its coefficients mod $p$ and consider its action on the field $ {{\mathbb{F}}}_p$. The questions of whether and in what sense these families are random have been studied extensively, spurred in part by Pollard’s famous “rho” algorithm for integer factorization (the heuristic justification of which is the conjectural randomness of one such family). However, the…

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