A Class of Discrete Spectra of Non-pisot Numbers

Abstract

We investigate the class of ±1 polynomials evaluated at q defined as: A(q) = { 0 + 1q + · · · + mq : i ∈ {−1, 1}} and usually called spectrum, and show that, if q is the root of the polynomial xn − xn−1 − · · · − xk+1 + xk + xk−1 + · · · + x + 1 between 1 and 2, and n > 2k + 3, then A(q) is discrete, which means that it does not have any accumulation points… (More)

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