Introduction to algorithms
Mathematics for computer algebra
Mathematics for computer algebra
A course in computational algebraic number theory
A course in computational algebraic number theory
On beta expansions for Pisot numbers
Mathematics of Computation
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Properties of Pisot numbers have long been of interest. One line of questioning, initiated by Erdös. Joó and Komornik in 1990. is the determination of l(q) for Pisot numbers q, where l(q) = inf(|y|:y = ε0 + ε1q1 + ...+ εnqn, εi ∈ {±1,0}, y ≠ 0.) Although the quantity l(q) is known for some Pisot numbers q, there has been no general method for computing l(q). This paper gives such an algorithm. With this algorithm, some properties of l(q) and its generalizations are investigated.A related question concerns the analogy of l(q), denoted a(q), where the coefficients are restricted to ±1; in particular, for which non-Pisot numbers is a(q) nonzero? This paper finds an infinite class of Salem numbers where a(q) ≠ 0.