On the Davenport-Mahler Bound

ESCORCIELO PAULA ; PERRUCCI DANIEL

Atlanta

Conferencia; SIAM Conference on Applied Algebraic Geometry; 2017

SIAM

The Davenport-Mahler bound is a lower bound for the product of the lengths of the edges on a graph whose vertices are the complex roots of a univariate polynomial, under certain assumptions. Roughly speaking, this bound makes evident an interaction between the involved lengths, in the sense that not all of them can be simultaneously very small. In this talk, we will show that by considering divided differences, the Davenport-Mahler bound can be extended to arbitrary graphs with vertices on the set of roots of a given univariate polynomial, and we show some applications.