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Campbell, Douglas Houghton; Ferguson, Helaman; Forcade, Rodney W.

doi:10.1512/iumj.1983.32.32037

Cited by 7 publications

(16 citation statements)

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“…We next try u 2 = 2. This means (2.1) that D 3 (z) = 1 + z 2 − z 3 and E 3 (z) = 1 − z − z 3 , implying that w 3 = 2. Also, by (2.3) and (2.4) we have D + 3 (z) = 1 − 2z − 3z 2 + z 3 and E + 3 (z) = 1 − 3z − 2z 2 + z 3 , and so w + 3 = 8.…”

Section: Lemma 32 Suppose Fmentioning

confidence: 99%

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Pisot Numbers from {0, 1}-Polynomials

Mukunda¹

2010

Can. math. bull.

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A Pisot number is a real algebraic integer greater than 1, all of whose conjugates lie strictly inside the open unit disk; a Salem number is a real algebraic integer greater than 1, all of whose conjugate roots are inside the closed unit disk, with at least one of them of modulus exactly 1. Pisot numbers have been studied extensively, and an algorithm to generate them is well known. Our main result characterises all Pisot numbers whose minimal polynomial is derived from a Newman polynomial — one with {0, 1}-coefficients — and shows that they form a strictly increasing sequence with limit (1 + √5)/2. It has long been known that every Pisot number is a limit point, from both sides, of sequences of Salem numbers. We show that this remains true, from at least one side, for the restricted sets of Pisot and Salem numbers that are generated by Newman polynomials.

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Section: Lemma 32 Suppose Fmentioning

confidence: 99%

“…A Newman polynomial [3] is a polynomial with both constant term and leading coefficient equal to 1, and whose remaining coefficients are all either 0 or 1. In this paper we consider Newman polynomials that give rise to either Pisot numbers or Salem numbers.…”

Section: Introductionmentioning

confidence: 99%

Pisot Numbers from {0, 1}-Polynomials

Mukunda¹

2010

Can. math. bull.

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“…In fact, it was shown in [7] that min |z| =1 |P 12 (z)|=c 0 >1.36. Following C. Smyth [14] one then defines inductively…”

Section: Discrepancymentioning

confidence: 99%

On Uniformly Distributed Dilates of Finite Integer Sequences

Konyagin

Ruzsa

Schlag

2000

Journal of Number Theory

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“…Erdös [1] and Littlewood [2] asked several questions concerning the minimum modulus of P(z) on the unit circle, under various restrictions of the coefficients a¡, e.g., \af\ -1 for j = 1, 2, ... , n . If we insist that a¡• = 1 for j = 2, ... ,n and rx -0, then P(z) is a Newman polynomial, as defined by Campbell, Ferguson, and Forcade [3]. Many other authors have investigated the minimum modulus of Newman polynomials, most notably Smyth [4] and Boyd [5].…”

Section: Introductionmentioning

confidence: 99%