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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2012

Author dc:creator

• Tran, Khang

Contributors dc:contributor

• Stolarsky, Kenneth B.
• Berndt, Bruce C.
• Zaharescu, Alexandru
• Hildebrand, A.J.

• discriminant
• resultant
• root distribution

Statement dc:rights

• Copyright 2012 Khang D. Tran

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/34354

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/34354