Title:Multiplicative dependence and independence of the translations of algebraic numbers

Time: Thu, Oct. 20, 2016, AM 9:00-10:00

Speaker:Dr. Min Sha (Macquarie University Australia)

Location:Room 4318, Building No.4, Wushan Campus

Abstract:We say that non-zero complex numbers a_1,...,a_n are multiplicatively dependent if there exist integers k_1,...,k_n, not all zero, such that a_1^{k_1} ···a_n^{k_n} = 1. In this talk, we first present that given pairwise distinct algebraic numbers a_1, . . . , a_n, the numbers a_1 + t, . . . , a_n + t are multiplicatively independent for all sufficiently large integers t. Then, for a pair (a,b) of distinct integers, we will say something about how many pairs (a + t, b + t) are multiplicatively dependent when t runs through the integers. This is joint work with Arturas Dubickas.