Number Theory
Complex Pisot numbers of small modulus
Comptes Rendus. Mathématique, Volume 336 (2003) no. 12, pp. 967-970.

We use an algorithm of Chamfy to determine all complex Pisot numbers of modulus less than 1.17.

Nous utilisons une méthod de Chamfy pour déterminer les nombres de Pisot imaginaires de module au plus 1.17.

Received:
Accepted:
Published online:
DOI: 10.1016/S1631-073X(03)00236-X
Garth, David 1

1 Division of Mathematics and Computer Science, Truman State University, Kirksville, MO 63501, USA
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Garth, David. Complex Pisot numbers of small modulus. Comptes Rendus. Mathématique, Volume 336 (2003) no. 12, pp. 967-970. doi : 10.1016/S1631-073X(03)00236-X. http://www.numdam.org/articles/10.1016/S1631-073X(03)00236-X/

[1] Bertin, M.J.; Decomps-Guilloux, A.; Grandet-Hugot, M.; Pathiaux-Delefosse, M.; Schreiber, J.P. Pisot and Salem Numbers, Birkhäuser, Basel, 1992

[2] Boyd, D.W. Pisot and Salem numbers in intervals of the real line, Math. Comp., Volume 32 (1978) no. 144, pp. 1244-1260

[3] Cantor, D.G. On sets of algebraic integers whose remaining conjugates lie in the unit circle, Trans. Amer. Math. Soc., Volume 105 (1962), pp. 391-406

[4] Chamfy, C. Fonctions méromorphes dans le cercle-unité et leurs séries de Taylor, Ann. Inst. Fourier, Volume 8 (1958), pp. 211-251

[5] Dufresnoy, J.; Pisot, Ch. Sur un ensemble fermé d'entiers algébriques, Ann. Sci. École Norm. Sup. (3), Volume 70 (1953), pp. 105-133

[6] Dufresnoy, J.; Pisot, Ch. Étude de certaines fonctions méromorphes bornées sur le cercle unité, application á un ensemble fermé d'entiers algébriques, Ann. Sci. École Norm. Sup. (3), Volume 72 (1955), pp. 69-72

[7] D. Garth, Small limit points of sets of algebraic integers, Dissertation, Kansas State University, May 2000

[8] Samet, P.A. Algebraic integers with two conjugates outside the unit circle, Proc. Cambridge Philos. Soc., Volume 49 (1953), pp. 421-436

[9] Siegel, C.L. Algebraic integers whose conjugates lie in the unit circle, Duke Math. J., Volume 11 (1944), pp. 597-602

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