Director of Research (if dissertation) or Advisor (if thesis)
Reznick, Bruze
Doctoral Committee Chair(s)
Hinkkanen, Aimo
Committee Member(s)
Boca, Florin
Hildebrand, AJ
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
polynomials
stern polynomials
continued fractions
Abstract
In this dissertation, we study a polynomial analogue of the Stern sequence originally introduced by Klavžar, Milutinović, and Petr. Through algebraic, combinatorial, and geometric means, we prove several results about the coefficients and zeros of these polynomials, with a special emphasis on subsets of C which cannot contain any zeros. We conclude with a discussion about polynomials with coefficients in the set {0, 1, ..., a}, where a ≥ 1 is a positive integer.
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