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arXiv · 1704.00463

Discriminants of a Class of Self-inversive Polynomials and Real Binary Forms

Keisuke Uchimura
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Abstract

A class of self-inversive polynomials includes all the self-reciprocal polynomials. Let A denote the set of all self-reciprocal polynomials with n+1 coefficients. Let B denote the set of certain self-inversive and non self-reciprocal polynomials with n+1 coefficients for odd n. Let C denote the set of real binary n-ic forms. Then there exist a bijection between A and C and another bijection between B and C. Let f be a monic polynomial in A and g be the corresponding polynomial in C. If the reading coefficient of g is not zero, then the discriminant of g is expressed by the determinant of a matrix of type (n, n). Any element of the matrix is a polynomial in the coefficients of f with integer coefficients. The same holds for monic polynomials in B.

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Keisuke Uchimura. 2017-04-03. Discriminants of a Class of Self-inversive Polynomials and Real Binary Forms. https://arxiv.org/abs/1704.00463

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