No CrossRef data available.
Article contents
Sequences of integers satisfying congruence relations and Pisot-Vijayaraghavan numbers
Published online by Cambridge University Press: 09 April 2009
Extract
Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.
We consider infinite sequences 
of positive integers having exponential growth: 
and becoming ultimately periodic modulo each member of a rather sparse infinite set of integers. If sufficient, natural conditions are placed on the growth and periodicities of , we find that a is an algebraic integer having all its algebraic conjugates within or on the unit circle, and fn has a special representation involving an. The result is a kind of dual to the theorem of Pisot (cf. Salem [2], p. 4, Theorem A).
- Type
- Research Article
- Information
- Copyright
- Copyright © Australian Mathematical Society 1967
References
[1]Cassels, J. W. S., An introduction to Diophantine approximation (Cambridge Tracts in Mathematics and Mathematical Physics, 45, Cambridge University Press, Cambridge, 1957).Google Scholar
You have
Access