Functional Analysis and Applications Seminar 

13/05/2011, 15:00 — 16:00 — Room P3.10, Mathematics Building
Konstantin Dyakonov, ICREA e Universitat de Barcelona

Zeros of analytic functions, with or without multiplicities

The so-called abc theorem for polynomials, also known as Mason's or Mason-Stothers' theorem, deals with nontrivial polynomial solutions to the Diophantine equation \(a+b=c\). It provides a lower bound on the number of distinct zeros of the polynomial abc in terms of the degrees of \(a\), \(b\) and \(c\). We prove some "local" \(abc\) type theorems for general analytic functions living on a (reasonably nice) bounded domain rather than on the whole plane. The estimates obtained are sharp, for any domain, and they imply a generalization of the original "global" \(abc\) theorem by a limiting argument.