Search bounds for zeros of polynomials over the algebraic closure of Q

Lenny Fukshansky

Published 2005-12-06, updated 2006-10-06Version 2

We discuss existence of explicit search bounds for zeros of polynomials with coefficients in a number field. Our main result is a theorem about the existence of polynomial zeros of small height over the field of algebraic numbers outside of unions of subspaces. All bounds on the height are explicit.