Number Theory Seminar

Speaker: Shanta Laishram (ISI Delhi)

Title: On the stability of certain higher degree polynomials.

Abstract: We study the stability of $f(z)=z^d+\frac{1}{c}$ for $d\geq 3$, $c\in{\mathbb{Z}\setminus\{0\}}$. We show that whenever $f(z)$ is irreducible over $\mathbb{Q}$, all its iterates are irreducible over $\mathbb{Q}$, that is, $f(z)$ is stable over $\mathbb{Q}$ for infinitely many values of $d$. This is a joint work with R. Sarma and H. Sharma.