ALGEBRAIC PROPERTIES OF WEAK PERRON NUMBERS

Brunotte, Horst

doi:10.2478/tmmp-2013-0023

Abstract

We study algebraic properties of real positive algebraic numbers which are not less than the moduli of their conjugates. In particular, we are interested in the relation of these numbers to Perron numbers.

References

[1] BOYD, D. W.: The maximal modulus of an algebraic integer, Math. Comp. 45 (1985), 243-249.10.1090/S0025-5718-1985-0790657-8
Search in Google Scholar
[2] DUBICKAS, A.: A note on powers of Pisot numbers, Publ. Math. Debrecen 56 (2000), 141-144.
Search in Google Scholar
[3] DUBICKAS, A.: Mahler measures generate the largest possible groups, Math. Res. Lett. 11 (2004), 279-283.10.4310/MRL.2004.v11.n3.a1
Search in Google Scholar
[4] DUBICKAS, A.-SMYTH, C. J.: On the Remak height, the Mahler measure and conjugate sets of algebraic numbers lying on two circles, Proc. Edinburgh Math. Soc. (2) 44 (2001), 1-17.10.1017/S001309159900098X
Search in Google Scholar
[5] FERGUSON, R.: Irreducible polynomials with many roots of equal modulus., Acta Arith. 78 (1997), 221-225.10.4064/aa-78-3-221-225
Search in Google Scholar
[6] JURKAT, W.-KRATZ, W.-PEYERIMHOFF, A.: On best two-dimensional Dirichlet- -approximations and their algorithmic calculation, Math. Ann. 244 (1979), 1-32.10.1007/BF01420334
Search in Google Scholar
[7] JUST, B.: Generalizing the continued fraction algorithm to arbitrary dimensions, SIAM J. Comput. 21 (1992), 909-926.10.1137/0221054
Search in Google Scholar
[8] KENYON, R.: The construction of self-similar tilings, Geom. Funct. Anal. 6 (1996), 471-488.10.1007/BF02249260
Search in Google Scholar
[9] KOREC, I.: Irrational speeds of configurations growth in generalized Pascal triangles, Theoret. Comput. Sci. 112 (1993), 399-412.10.1016/0304-3975(93)90029-S
Search in Google Scholar
[10] , Open problems more or less related to generalized Pascal triangles, Preprint 22/1996, Mathematical Institute SAS, Bratislava.
Search in Google Scholar
[11] LIND, D. A.: The entropies of topological Markov shifts and a related class of algebraic integers, Ergodic Theory Dynam. Systems 4 (1984), 283-300.10.1017/S0143385700002443
Search in Google Scholar
[12] , Entropies of automorphisms of a topological Markov shift, Proc. Amer. Math.Soc. 99 (1987), 589-595.10.1090/S0002-9939-1987-0875406-0
Search in Google Scholar
[13] LIND, D.-MARCUS, B.: An Introduction to Symbolic Dynamics and Coding. Cambridge University Press, Cambridge, 1995.10.1017/CBO9780511626302
Search in Google Scholar
[14] SCHINZEL, A.: A class of algebraic numbers, Tatra Mt. Math. Publ. 11 (1997), 35-42.
Search in Google Scholar
[15] VERGER-GAUGRY, J.-L.: Uniform distribution of Galois conjugates and beta-conjugates of a Parry number near the unit circle and dichotomy of Perron numbers, Unif.Distrib. Theory 3 (2008), 157-190.
Search in Google Scholar
[16] WU, Q.: The smallest Perron numbers, Math. Comp. 79 (2010), 2387-2394.10.1090/S0025-5718-10-02345-8
Search in Google Scholar

ALGEBRAIC PROPERTIES OF WEAK PERRON NUMBERS

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