Discriminants: calculation, properties, and connection to the root distribution of polynomials with rational generating functions

This research centers on discriminants and how discriminants and their q-analogues relate to the root distribution of polynomials. This topic includes the connections between the root distribution of a sequence of polynomials and the discriminant of the denominator of its generating function. A more specialized aspect of this area of this research concerns the root distribution and the generating functions of the discriminants of polynomials related to Chebyshev polynomials. Other areas involve the factorization properties and asymptotic behaviors of q-analogues of discriminants of cubic polynomials, and the diagonal sequence of the resultant of a certain pair of reciprocal polynomials