# 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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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 $\|.\|_{A}$.