Brigham Young University, Provo, Utah 84602, U.S.A.
Bibliografia
M. J. Bertin, A. Decomps-Guilloux, M. Grandet-Hugot, M. Pathiaux-Delefosse and J. P. Schreiber (1992), Pisot and Salem Numbers, Birkhäuser, Boston.
D. Boyd (1969), Transcendental numbers with badly distributed powers, Proc. Amer. Math. Soc. 23, 424-427.
G. Choquet (1981), θ-fermés et dimension de Hausdorff. Conjectures de travail. Arithmétique des θ-cycles (θ = 3/2), C. R. Acad. Sci. Paris Sér. I 292, 339-344.
L. Flatto (1992), Z-numbers and β-transformations, in: Symbolic Dynamics and Its Applications, P. Walters (ed.), Contemp. Math. 135, Amer. Math. Soc., Providence, R.I., 181-202.
L. Flatto and J. C. Lagarias (1994), The lap counting function for linear mod one transformations, I. Explicit formulas and renormalizability, Ergodic Theory Dynamical Systems, to appear.
L. Flatto, J. C. Lagarias and B. Poonen (1994), The zeta function of the beta transformation, Ergodic Theory Dynamical Systems 14, 237-266.
K. Mahler (1968), An unsolved problem on the powers of 3/2, J. Austral. Math. Soc. 8, 313-321.
W. Parry (1960), On the β-expansion of real numbers, Acta Math. Acad. Sci. Hungar. 11, 401-416.
C. Pisot (1938), La répartition modulo 1 et les nombres algébriques, Ann. Scuola Norm. Sup. Pisa (2) 7, 204-248.
C. Pisot (1946), Répartition (mod 1) des puissances successives des nombres réels, Comment. Math. Helv. 19, 153-160.
A. Pollington (1978), Intervals Constructions in the Theory of Numbers, Ph.D. thesis, University of London.
A. D. Pollington (1979), On the density of sequences {nₖξ}, Illinois J. Math. 23, 511-515.
A. D. Pollington (1981), Progressions arithmétiques généralisées et le problème des (3/2)ⁿ, C. R. Acad. Sci. Paris Sér. I 292, 383-384.
A. Rényi (1957), Representations for real numbers and their ergodic properties, Acta Math. Acad. Sci. Hungar. 8, 472-493.
R. Tijdeman (1972), Note on Mahler's 3/2-Problem, K. Norske Vidensk. Selsk. Skr. 16, 1-4.
T. Vijayaraghavan (1940), On the fractional parts of the powers of a number, I, J. London Math. Soc. 15, 159-160.
T. Vijayaraghavan (1941), On the fractional parts of the powers of a number, II, Proc. Cambridge Philos. Soc. 37, 349-357.
T. Vijayaraghavan (1942), On the fractional parts of the powers of a number, III, J. London Math. Soc. 17, 137-138.
T. Vijayaraghavan (1948), On the fractional parts of powers of a number, IV, J. Indian Math. Soc. (N.S.) 12, 33-39.
Typ dokumentu
Bibliografia
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