Pólya's Theorem with zeros

Pólya's Theorem says that if p is a homogeneous polynomial in n variables which is positive on the standard n-simplex, and F is the sum of the variables, then for a sufficiently large exponent N, F^N * p has positive coefficients. Pólya's Theorem has had ...

Let R[X]:=R[X"1,...,X"n]. Polya's Theorem says that if a form (homogeneous polynomial) p@?R[X] is positive on the standard n-simplex @D"n, then for sufficiently large N all the coefficients of (X"1+...+X"n)^Np are positive. The work in this paper is ...

Let f(x) and g(x) be two real polynomials whose leading coefficients have the same sign. Suppose that f(x) and g(x) have only real zeros and that g interfaces f or g alternates left of f. We show that if ad ≥ bc then the polynomial (bx + a)f(x) + (dx + ...