Extremal values of continuants and transcendence of certain continued fractions

Advances in Applied Mathematics

Volumn 32, Issue 4, 2004, Pages 754-790

  Baxa, Christoph ^a  

^a UNIVERSITY OF VIENNA   (Austria)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 2442676235     PISSN: 01968858     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0196-8858(03)00103-9     Document Type: Article

References (13)

1. J.-P. Allouche, J.L. Davison, M. Queffélec, L.Q. Zamboni, Transcendence of Sturmian or morphic continued fractions, J. Number Theory 91 (2001) 39-66.
2. C. Baxa, J. Schoißengeier, Calculation of improper integrals using (nα)-sequences, Monatsh. Math. 135 (2002) 265-277.
3. J.L. Davison, A class of transcendental numbers with bounded partial quotients, in: R.A. Mollin (Ed.), Number Theory and Applications, Kluwer, Dordrecht, 1989, pp. 365-371.
4. J.L. Davison, Continued fractions with bounded partial quotients, Proc. Edinburgh Math. Soc. 45 (2002) 653-671.
5. C. Faivre, Distribution of Lévy constants for quadratic numbers, Acta Arith. 61 (1992) 13-34.
6. C. Faivre, The Lévy constant of an irrational number, Acta Math. Hungar. 74 (1997) 57-61.
7. J.H. Halton, The distribution of the sequence {nξ} (n = 0, 1, 2,...), Proc. Cambridge Philos. Soc. 61 (1965) 665-670.
8. H. Jager, P. Liardet, Distributions arithmétiques des dénominateurs de convergents de fractions continues, Indag. Math. 50 (1988) 181-197.
9. L. Kuipers, H. Niederreiter, Uniform Distribution of Sequences, Wiley, New York-London-Sydney-Toronto, 1974.
10. O. Perron, Die Lehre von den Kettenbrüchen, Band 1, Teubner, Stuttgart, 1977.
11. M. Queffélec, Irrational numbers with automaton-generated continued fraction expansion, in: J.-M. Gainbaudo, P. Hubert, P. Tisseur, S. Vaienti (Eds.), Dynamical Systems (Luminy-Marseille, 1998), World Scientific, River Edge, NJ, 2000, pp. 190-198.
12. G. Ramharter, Extremal values of continuants, Proc. Amer. Math. Soc. 89 (1983) 189-201.
13. W.M. Schmidt, On simultaneous approximations of two algebraic numbers by irrationals, Acta Math. 119 (1967) 27-50.