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.
© 2009 Rocky Mountain Mathematics Consortium
Fukshansky, Lenny. "Search Bounds for Zeros of Polynomials over the Algebraic Closure of Q." Rocky Mountain Journal of Mathematics 39.3 (2009): 789-804. doi: 10.1216/RMJ-2009-39-3-789