On stable quadratic polynomials

**Speaker:** Dr. Omran Ahmadi (UCD)

**Time:** 4:00PM

**Date:** Thu 1st March 2012

**Location:** Mathematical Sciences Seminar Room (Ag 1.01)

**Abstract**

A polynomial f(X) in K[X] over a field K is called stable if all its iterates are irreducible over K. We show that almost all monic quadratic polynomials f(X) in Z[X] are stable over Q. We also show that the presence of squares in so-called critical orbits of a quadratic polynomial f(X) in Z[X] can be detected by a finite algorithm; this property is closely related to the stability of f(X). We also prove there are no stable quadratic polynomials over finite fields of characteristic 2 but they exist over some infinite fields of characteristic 2.

(This talk is part of the K-Theory, Quadratic Forms and Number Theory series.)

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