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

Tran, Khang

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https://hdl.handle.net/2142/34354 Copy

Description

Title

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

Author(s)

Tran, Khang

Issue Date

2012-09-18T21:12:53Z

Director of Research (if dissertation) or Advisor (if thesis)

Stolarsky, Kenneth B.

Doctoral Committee Chair(s)

Berndt, Bruce C.

Committee Member(s)

• Stolarsky, Kenneth B.
• Zaharescu, Alexandru
• Hildebrand, A.J.

Department of Study

Mathematics

Discipline

Mathematics

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• discriminant
• resultant
• root distribution

Abstract

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.

Graduation Semester

2012-08

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

Copyright and License Information

Copyright 2012 Khang D. Tran

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