Geodesic
Schur-Szegö Composition of Small Degree Polynomials
Serdica Mathematical Journal, Tome 40 (2014) no. 2, pp. 111-128.

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We consider real polynomials in one variable without root at 0 and without multiple roots. Given the numbers of the positive, negative and complex roots of two such polynomials, what can be these numbers for their composition of Schur-Szegö? We give the exhaustive answer to the question for degree 2, 3 and 4 polynomials and also in the case when the degree is arbitrary, the composed polynomials being with all roots real, and one of the polynomials having all roots but one of the same sign. 2010 Mathematics Subject Classification: 12D10.
Keywords: real polynomial, composition of Schur-Szegö, real (positive/negative) root 
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Kostov, Vladimir Petrov. Schur-Szegö Composition of Small Degree Polynomials. Serdica Mathematical Journal, Tome 40 (2014) no. 2, pp. 111-128. http://geodesic.mathdoc.fr/item/SMJ2_2014_40_2_a1/