Counting integer polynomials with multiplicatively dependent roots

Min Sha

Affiliation:

Macquarie University

Date:

Thu, 02/03/2017 - 2:00pm

Venue:

RC-4082, The Red Centre, UNSW

Abstract:

We call non-zero complex numbers $z_1, \ldots, z_n$ multiplicatively dependent if there exist integers $k_1, \ldots, k_n$, not all zero, such that $z_1^{k_1} \cdots z_n^{k_n}=1$. The multiplicative relations in conjugate algebraic numbers have been studied for a long time from various aspects. In this talk, I will present some recent results about the number of integer polynomials with fixed degree and bounded height and whose roots are multiplicatively dependent. (This is joint work with Arturas Dubickas.)