Abstract
We first prove two theorems that are very useful for studying the convergence properties of certain rational sequences used in the succeeding sections.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
M.J. Bertin, Nouvelles applications d’un théorème de Pisot, Groupe d’étude en théorie analytique des nombres, Publications de l’I.H.P. 1 ère et 2 ième année.
M. J. Bertin, Généralisation des suites de Pisot et de Boyd, Acta Arithm., 57, (1991), 211–223.
M.J. Bertin, Généralisation des suites de Pisot et de Boyd II, Acta Arithm., 59.3, (1991), 11–15.
D.W. Boyd, Pisot sequences which satisfy no linear recurrence, Acta Arithm., 32, (1977), 89–98.
D.W. Boyd, Some integer sequences related to Pisot sequences, Acta Arithm., 34, (1979), 295–305.
D.W. Boyd, Pisot sequences, Pisot numbers and Salem numbers, Soc. Math, de France. Astérisque, 61, (1979), 35–42.
D.W. Boyd, On linear recurrence relations satisfied by Pisot sequences, Acta Arithm., 47, (1986), 13–27.
D.W. Boyd, Which rationals are ratios of Pisot sequences? Canad. Math. Bull, 28, (1985), no3, 343–349.
D.W. Boyd, Pisot sequences which satisfy no linear recurrence II, Acta Arithm., 48, (1987), no2, 191–195.
D.W. Boyd, Non-recurrence of F(0, 30, 61), Private letter, April 23, 1987.
D.G. Cantor, On families of Pisot E-sequences, Ann. Sc. Ec. Norm. Sup., (4), 9, (1976), 283–308.
D.G. Cantor, Investigations of T-numbers and E-sequences in Computers in Number Theory, Ed. by A.O.L. Atkins and B.J. Birch Academic Press N.Y., (1971).
M.J. De Leon, Pisot sequences, J. Reine Angw. Math., 249, (1971), 20–30.
P. Flor, Über eine Klasse von Folgen naturlicher Zahlen, Math. Ann., 140, (1960), 299–307.
P. Galyean, On linear recurrence relations for E-sequences, Thesis, University of California, Los Angeles (1971).
Ch. Pisot, La répartition modulo 1 et les nombres algébriques, Scuola. Norm. Sup. Pisa, 7, (1938), 205–248.
R. Salem, Algebraic Numbers and Fourier Analysis, Heath Mathematical Monographs, Boston, (1963).
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1992 Springer Basel AG
About this chapter
Cite this chapter
Bertin, M.J., Decomps-Guilloux, A., Grandet-Hugot, M., Pathiaux-Delefosse, M., Schreiber, J.P. (1992). Pisot Sequences, Boyd Sequences and Linear Recurrence. In: Pisot and Salem Numbers. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8632-1_13
Download citation
DOI: https://doi.org/10.1007/978-3-0348-8632-1_13
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9706-8
Online ISBN: 978-3-0348-8632-1
eBook Packages: Springer Book Archive