Voir la notice de l'article provenant de la source Cambridge University Press
Dubickas, Artūras. Mahler Measures Close to an Integer. Canadian mathematical bulletin, Tome 45 (2002) no. 2, pp. 196-203. doi: 10.4153/CMB-2002-022-8
@article{10_4153_CMB_2002_022_8,
author = {Dubickas, Art\={u}ras},
title = {Mahler {Measures} {Close} to an {Integer}},
journal = {Canadian mathematical bulletin},
pages = {196--203},
year = {2002},
volume = {45},
number = {2},
doi = {10.4153/CMB-2002-022-8},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2002-022-8/}
}
[1] [1] Adler, R. L. and Marcus, B., Topological entropy and equivalence of dynamical systems. Mem. Amer. Math. Soc. (219) 20(1979). Google Scholar
[2] [2] Boyd, D. W., Reciprocal polynomials having small measure.Math. Comp. 35 (1980), 35–1980. Google Scholar
[3] [3] Boyd, D. W., Speculations concerning the range of the Mahler measure. Canad. Math. Bull. 24 (1981), 24–1981. Google Scholar
[4] [4] Boyd, D. W., Perron units which are not Mahler measures. Ergodic Theory Dynamical Systems 6 (1986), 6–1986. Google Scholar
[5] [5] Boyd, D. W., Reciprocal algebraic integers whose Mahler measures are non-reciprocal. Canad. Math. Bull. 30 (1987), 30–1987. Google Scholar
[6] [6] Boyd, D. W., Reciprocal polynomials having small measure. II. Math. Comp. 53 (1989), 53–1989. Google Scholar
[7] [7] Dobrowolski, E., On a question of Lehmer and the number of irreducible factors of a polynomial. Acta Arith. 34 (1979), 34–1979. Google Scholar
[8] [8] Dubickas, A., Algebraic conjugates outside the unit circle. In: New Trends in Probability and Statistics Vol. 4: Analytic and Probabilistic Methods in Number Theory, Palanga, 1996 (eds. A. Laurincikas et al.), TEV Vilnius, VSP Utrecht, 1997, 11–21. Google Scholar
[9] [9] Dubickas, A., Polynomials with a root close to an integer. Liet. Matem. Rink. 39 (1999), 39–1999. Google Scholar
[10] [10] Dubickas, A. and Smyth, C. J., On the Remak height, the Mahler measure, and conjugate sets of algebraic numbers lying on two circles. Proc. Edinburgh Math. Soc., to appear. Google Scholar
[11] [11] Everest, G. and Ward, T., Heights of polynomials and entropy in algebraic dynamics. Springer, London, 1999. Google Scholar
[12] [12] Kronecker, L., Zwei Sätze über Gleichungen mit ganzzahligen Coefficienten. J. Reine Angew. Math. 53 (1857), 53–1857. Google Scholar
[13] [13] Lehmer, D. H., Factorization of certain cyclotomic functions. Ann. of Math. 34 (1933), 34–1933. Google Scholar
[14] [14] Louboutin, R., Sur la mesure de Mahler d’un nombre algébrique. C. R. Acad. Sci. Paris 296 (1983), 296–1983. Google Scholar
[15] [15] Mossinghoff, M. J., Polynomials with small Mahler measure.Math. Comp. 67 (1998), 67–1998. Google Scholar
[16] [16] Perron, O., Neue Kriterien für die Irreduzibilität algebraischer Gleichungen. J. Reine Angew. Math. 132 (1907), 132–1907. Google Scholar
[17] [17] Selmer, E. S., On the irreducibility of certain trinomials. Math. Scand. 4 (1956), 4–1956. Google Scholar
[18] [18] Siegel, C. L., Algebraic integers whose conjugates lie in the unit circle. Duke Math. J. 11 (1944), 11–1944. Google Scholar
[19] [19] Smyth, C. J., On the product of conjugates outside the unit circle of an algebraic integer. Bull. London Math. Soc. 3 (1971), 3–1971. Google Scholar
[20] [20] Smyth, C. J., Topics in the theory of numbers. PhD Thesis, University of Cambridge, 1972. Google Scholar
[21] [21] Voutier, P., An effective lower bound for the height of algebraic numbers. Acta Arith. 74 (1996), 74–1996. Google Scholar
[22] [22] Waldschmidt, M., Sur le produit des conjugués extérieurs au cercle unité d’un entier algébrique. Enseign. Math. (2) 26 (1981), 26–1981. Google Scholar
[23] [23] Waldschmidt, M., Diophantine approximation on linear algebraic groups. Grundlehren Math.Wiss. 326, Springer, Berlin-Heidelberg, 2000. Google Scholar
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