Counting integer polynomials with multiplicatively dependent roots

Speaker: 

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.)

School Seminar Series: