Approximation by Polynomials with Coefficients ±1 Original Research Article

In response to a question of R. Kenyon, we prove that the set of polynomials with coefficients ±1, evaluated at a fixed real number θ, is dense in image for a.e. θset membership, variant(image, 2). For θset membership, variant(1, image], a more complete result can be obtained by elementary methods.