Datum:
Mit, 06/04/2016 - 16:30 - 17:30
Given a vector $v=(v_1, \ldots, v_n)$ of $n$ complex numbers, we
say that $v$ is multiplicatively dependent if there is a non-zero
integer vector $k=(k_1, \ldots, k_n)$ such that $v_1^{k_1} \cdots
v_n^{k_n}=1$. In this talk, I will present some recent results on
counting multiplicatively dependent vectors of algebraic numbers of
fixed degree (or within a number field) and bounded height. These
include sharp lower and upper bounds, and especially asymptotic formulas
for several cases. (This is joint work with Francesco Pappalardi, Igor
Shparlinski and Cameron Stewart.)