Number Theory Seminar

Date: January 31, 2018

Time: 1:15PM - 2:15PM

Location: BLOC 220

Speaker: Andrew Bridy, Texas A&M University

Title: The cycle structure of unicritical polynomials in finite fields

Abstract: Let f(x) = x^k+a in Z[x] for k \geq 2. Consider the family of dynamical systems given by the action of f on F_p as p varies among primes. The question of how and in what sense this family approximates a random family of dynamical systems has been studied extensively, motivated in part by Pollard's "rho" algorithm for integer factorization. We show that for most choices of a, the cycle structure in this family is "as random as possible" in an appropriate sense. As a corollary, we show that most members of these families have many cycles. This is joint work with Derek Garton.

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