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On some higher degree sign-definite multivariate polynomials associated with definite quadratic forms

Positive and negative quadratic forms are well known and widely used. They are multivariate homogeneous polynomials of degree two taking positive or negative values respectively for any values of their arguments not all zero. In the present paper a certain higher degree polynomial is associated with each quadratic form such that the form is definite if and only if this polynomial is sign-definite.