Coxeter groups, Salem numbers and the Hilbert metric
Publications Mathématiques de l'IHÉS, Tome 95 (2002), pp. 151-183 
@article{PMIHES_2002__95__151_0,
     author = {McMullen, Curtis T.},
     title = {Coxeter groups, {Salem} numbers and the {Hilbert} metric},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     pages = {151--183},
     year = {2002},
     publisher = {Institut des Hautes Etudes Scientifiques},
     volume = {95},
     mrnumber = {1953192},
     language = {en},
     url = {https://www.numdam.org/item/PMIHES_2002__95__151_0/}
}
TY  - JOUR
AU  - McMullen, Curtis T.
TI  - Coxeter groups, Salem numbers and the Hilbert metric
JO  - Publications Mathématiques de l'IHÉS
PY  - 2002
SP  - 151
EP  - 183
VL  - 95
PB  - Institut des Hautes Etudes Scientifiques
UR  - https://www.numdam.org/item/PMIHES_2002__95__151_0/
LA  - en
ID  - PMIHES_2002__95__151_0
ER  - 
%0 Journal Article
%A McMullen, Curtis T.
%T Coxeter groups, Salem numbers and the Hilbert metric
%J Publications Mathématiques de l'IHÉS
%D 2002
%P 151-183
%V 95
%I Institut des Hautes Etudes Scientifiques
%U https://www.numdam.org/item/PMIHES_2002__95__151_0/
%G en
%F PMIHES_2002__95__151_0
McMullen, Curtis T. Coxeter groups, Salem numbers and the Hilbert metric. Publications Mathématiques de l'IHÉS, Tome 95 (2002), pp. 151-183. https://www.numdam.org/item/PMIHES_2002__95__151_0/

[A'C] N. A'Campo. Sur les valeurs propres de la transformation de Coxeter. Invent. Math. 33 (1976), 61-67. | Zbl

[BW] H. S. Bear and M. L. Weiss. An intrinsic metric for parts. Proc. Amer. Math. Soc. 18 (1967), 812-17. | Zbl | MR

[BLM] S. Berman, Y. S. Lee, and R. V. Moody. The spectrum of a Coxeter transformation, affine Coxeter transformations, and the defect map. J. Algebra 121 (1989), 339-357. | Zbl | MR

[Bou] N. Bourbaki. Groupes et algèbres de Lie, Ch. IV-VI. Hermann, 1968; Masson, 1981. | Zbl

[B1] D. Boyd. Small Salem numbers. Duke Math. J. 44 (1977), 315-328. | Zbl | MR

[B2] D. Boyd. Pisot and Salem numbers in intervals of the real line. Math. Comp. 32 (1978), 1244-1260. | Zbl | MR

[B3] D. Boyd. Reciprocal polynomials having small measure. II. Math. Comp. 53 (1989), 355-357. | Zbl | MR

[Bus] H. Busemann. The Geometry of Geodesics. Academic Press, 1955. | Zbl | MR

[BK] H. Busemann and P. J. Kelly. Projective Geometry and Projective Metrics. Academic Press, 1953. | Zbl | MR

[CW] J. W. Cannon and Ph. Wagreich. Growth functions of surface groups. Math. Ann. 293 (1992), 239-257. | Zbl | MR

[Co] A. J. Coleman. Killing and the Coxeter transformation of Kac-Moody algebras. Invent. Math. 95 (1989), 447-477. | Zbl | MR

[CS] J. H. Conway and N. J. A. Sloane. Sphere Packings, Lattices and Groups. Springer-Verlag, 1999. | Zbl | MR

[CR] D. Cvetkovic and P. Rowlinson. The largest eigenvalue of a graph: a survey. Linear and Multilinear Algebra 28 (1990), 3-33. | Zbl | MR

[DP] J. Dufresnoy and Ch. Pisot. Etude de certaines fonctions méromorphes bornées sur le cercle unité. Application à un ensemble fermée d'entiers algébriques. Ann. Sci. Ecole Norm. Sup. 72 (1955), 69-92. | Zbl | Numdam

[FGR] V. Flammang, M. Grandcolas, and G. Rhin. Small Salem numbers. In Number Theory in Progress, Vol. I, pages 165-168. de Gruyter, 1999. | Zbl | MR

[Fl] W. J. Floyd. Growth of planar Coxeter groups, P.V. numbers, and Salem numbers. Math. Ann. 293 (1992), 475-483. | Zbl | MR

[FP] W. J. Floyd and S. P. Plotnick. Growth functions on Fuchsian groups and the Euler characteristic. Invent. Math. 88 (1987), 1-29. | Zbl | MR

[GH] E. Ghate and E. Hironaka. The arithmetic and geometry of Salem numbers. Bull. Amer. Math. Soc. 38 (2001), 293-314. | Zbl | MR

[GM] B. Gross and C. Mcmullen. Automorphisms of even unimodular lattices and unramified Salem numbers. To appear, J. Algebra. | Zbl | MR

[HH] L. Halbeisen and N. Hungerbühler. On periodic billiard trajectories in obtuse triangles. SIAM Rev. 42 (2000), 657-670. | Zbl | MR

[Ha1] P. De La Harpe. An invitation to Coxeter groups. In Group Theory from a Geometrical Viewpoint (Trieste, 1990), pages 193-253. World Sci. Publishing, 1991. | Zbl | MR

[Ha2] P. De La Harpe. On Hilbert's metric for simplices. In Geometric Group Theory, Vol. 1 (Sussex, 1991), pages 97- 119. Cambridge University Press, 1993. | Zbl

[H] D. Hilbert. Uber die gerade Linie als kürzeste Verbindung zweier Punkte. Math. Ann. 46 (1895), 91-96. | JFM

[Hir] E. Hironaka. The Lehmer polynomial and pretzel links. Canad. Math. Bull. 44 (2001), 440-451. | Zbl | MR

[Hof] A. J. Hoffman. On limit points of spectral radii of non-negative symmetric integral matrices. In Graph Theory and Applications, volume 303 of Lecture Notes in Mathematics, pages 165-17. Springer-Verlag, 1972. | Zbl | MR

[How] R. B. Howlett. Coxeter groups and M-matrices. Bull. London Math. Soc. 14 (1982), 137-141. | Zbl | MR

[Hum] J. E. Humphreys. Reflection Groups and Coxeter Groups. Cambridge University Press, 1990. | Zbl | MR

[Leh] D. H. Lehmer. Factorization of certain cyclotomic functions. Ann. of Math. 34 (1933), 461-479. | Zbl | MR

[MRS] J. F. MCKEE, P. ROWLINSON, and C. J. SMYTH. Pisot numbers from stars. In Number Theory in Progress, Vol. I, pages 309-319. de Gruyter, 1999. | Zbl | MR

[Mos] M. J. Mossinghoff. Polynomials with small Mahler measure. Math. Comp. 67 (1998), 1697-1705. | Zbl | MR

[Par] W. Parry. Growth series of Coxeter groups and Salem numbers. J. Algebra 154 (1993), 406-415. | Zbl | MR

[RT] H. Rademacher and O. Toeplitz. The Enjoyment of Mathematics. Dover, 1990. | Zbl

[Sa] R. Salem. Algebraic Numbers and Fourier Analysis. Wadsworth, 1983. | Zbl | MR

[Sh] J. B. Shearer. On the distribution of the maximum eigenvalue of graphs. Linear Algebra Appl. 114/115 (1989), 17-20. | Zbl | MR

[Vin1] E. B. Vinberg. Discrete groups that are generated by reflections. Math. USSR Izv. 5 (1971), 1083-1119. | Zbl

[Vin2] E. B. Vinberg. Some arithmetical discrete groups in Lobacevskii spaces. In Discrete subgroups of Lie groups and applications to moduli (Bombay, 1973), pages 323-348. Oxford Univ. Press, 1975. | Zbl | MR