Published online by Cambridge University Press: 09 April 2009
Let f(x) and g(x) be two polynomials with arbitrary complex coefficients that are relatively prime. Hence the maximum is positive for all complex x. Since m(x) is continuous and tends to infinity with |x|, the quantity E(f, g) = min m(x) is therefore also positive.
1 Approximation of algebraic numbers by algebraic numbers, Michigan Math. J. 8 (1961), 149–159.