Irreducibility of Iterates of a Second Degree Function

Author

Katharine Chamberlin, College of the Holy Cross

Date of Creation

5-16-2012

Document Type

Departmental Honors Thesis - Restricted Access

Department

Mathematics

First Advisor

Rafe Jones

Abstract

For most rational numbers q, all iterates of the polynomial f(x) = x2 - q,are irreducible. Yet, there is an infinite set of q such that f(x) is reducible, and an infinite set of q such that the second iterate, f2(x), is reducible when f(x) is irreducible. We have identified the conditions which define these sets of rational numbers. Our main result is that for n ≥ 3 there are only finitely many q such that f2(x) is irreducible and fn+I(x) is reducible.

Comments

Reader: John B. Little

Recommended Citation

Chamberlin, Katharine, "Irreducibility of Iterates of a Second Degree Function" (2012). Math and Computer Science Honors Theses. 38.
https://crossworks.holycross.edu/math_honor/38