University of Illinois Urbana-Champaign

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

Tran, Khang

Content Files
Tran_Khang.pdf

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

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
Date of Ingest
2012-09-18T21:12:53Z
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
Permalink
http://hdl.handle.net/2142/34354
Copyright and License Information
Copyright 2012 Khang D. Tran

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