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Questions about Polynomials with $\{0,-1,+1\}$ Coefficients

Borwein, Peter and Erdelyi, Tamas and Kos, Geza (1995) Questions about Polynomials with $\{0,-1,+1\}$ Coefficients. [Preprint]

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      Abstract

      We are interested in problems concerning the location and multiplicity of zeros of polynomials with small integer coefficients. We are also interested in some of the approximation theoretic properties of such polynomials. Let $$\Cal{F}_n:=\left\{\sum_{i=0}^n {a_ix^i}: a_i \in \{-1,0,1\}\right\}$$ and let $$\Cal{A}_n:=\left\{\sum_{i=0}^n {a_ix^i}: a_i \in \{0,1\}\right\} \qquad \text{and} \qquad \Cal{B}_n:=\left\{\sum_{i=0}^n {a_ix^i}: a_i \in \{-1,1\}\right\}\,.$$ Throughout this paper the uniform norm on a set $A \subset {\Bbb R}$ is denoted by $\|.\|_{A}$.

      Item Type: Preprint
      Additional Information: pubdom FALSE
      Uncontrolled Keywords: transfinite diameter, integers, diophantine approximation, zero one coefficients, Chebyshev, polynomial
      Subjects: 11-xx Number theory > 11Bxx Sequences and sets
      11-xx Number theory > 11Jxx Diophantine approximation, transcendental number theory
      Faculty: UNSPECIFIED
      Depositing User: Users 1 not found.
      Date Deposited: 17 Nov 2003
      Last Modified: 21 Apr 2010 11:13
      URI: https://docserver.carma.newcastle.edu.au/id/eprint/110

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