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 |
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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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