Vol. 86, No. 2, 1980

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ISSN: 0030-8730
Approximation properties of polynomials with bounded integer coefficients

Vladimir Drobot and S. McDonald

Vol. 86 (1980), No. 2, 447–450
Abstract

For every fixed positive integea N, let 𝒫N denote the set of all polynomials p(x) = aixi where ai is an integer, |ai|N. For a fixed real number t set 𝒫N(t) = {p(t) : p ∈𝒫N}.

Theorem 1. Suppose 1 < t < N + 1 and t is not a root of map of the polynomials from 𝒫N. Then 𝒫N(t) is dense in R.

Theorem 2. If t is an S-number then 𝒫N(t) is discrete for every N.

Mathematical Subject Classification
Primary: 12A15, 12A15
Milestones
Received: 10 November 1978
Revised: 4 May 1979
Published: 1 February 1980
Authors
Vladimir Drobot
S. McDonald