Pisot numbers in the neighborhood of a limit point. II
David W. Boyd
Math. Comp. 43 (1984), 593-602
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Abstract: Let S denote the set of real algebraic integers greater than one, all of whose other conjugates lie within the unit circle. In an earlier paper, we introduced the notion of "width" of a limit point of S and showed that, if the width of is smaller than 1.28... then there is an algorithm for determining all members of S in a neighborhood of . Recently, we introduced the "derived tree" in order to deal with limit points of greater width. Here, we apply these ideas to the study of the limit point , the zero of outside the unit circle. We determine the smallest neighborhood of in which all elements of S other than satisfy one of the equations , where is one of , or . The endpoints , and are elements of S of degrees 23 and 42, respectively.
W. Boyd, Pisot and Salem numbers in intervals
of the real line, Math. Comp.
32 (1978), no. 144, 1244–1260. MR 0491587
(58 #10812), http://dx.doi.org/10.1090/S0025-5718-1978-0491587-8
W. Boyd, Pisot numbers in the neighbourhood of a limit point.
I, J. Number Theory 21 (1985), no. 1,
804914 (87c:11096a), http://dx.doi.org/10.1016/0022-314X(85)90010-1
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Pisot, Etude de certaines fonctions méromorphes
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fermé d’entiers algébriques, Ann. Sci. Ecole Norm.
Sup. (3) 72 (1955), 69–92 (French). MR 0072902
- D. W. Boyd, "Pisot and Salem numbers in intervals of the real line," Math. Comp., v. 32, 1978, pp. 1244-1260. MR 0491587 (58:10812)
- D. W. Boyd, "Pisot numbers in the neighbourhood of a limit point. I," (To appear.) MR 804914 (87c:11096a)
- J. Dufresnoy & Ch. Pisot, "Étude de certaines fonctions méromorphes bornées sur le cercle unité, application à un ensemble fermé d'entiers algébriques," Ann. Sci. École Norm. Sup. (3), v. 72, 1955, pp. 69-92. MR 0072902 (17:349d)
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