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

Abstract

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.

10 pages, revised version: to appear in Rocky Mountain Journal of Mathematics; minor editorial revisions, removed section 5 for brevity of exposition

Cited by in corpus (1)

• Small zeros of quadratic forms over the algebraic closure of Q