The minimum root separation of a polynomial
George Ernest Collins, Ellis Horowitz · Mathematics of Computation · 1974
The minimum root separation of a complex polynomial A is defined as the minimum of the distances between distinct roots of A . For polynomials with Gaussian integer coefficients and no multiple roots, three lower bounds are derived for the root separation. In each case, the bound is a function of the degree n of A and the sum d of the absolute values of the coefficients of A . The notion of a seminorm for a commutative ring is defined, and it is shown how any seminorm can be extended to polynomial rings and matrix rings, obtaining a very general analogue of Hadamard’s determinant theorem.