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THERE ARE ONLY ELEVEN SPECIAL PISOT NUMBERS

Published online by Cambridge University Press:  01 January 1999

C. J. SMYTH
C. J. SMYTH
Affiliation:
Department of Mathematics and Statistics, The University of Edinburgh, James Clerk Maxwell Building, King's Buildings, Mayfield Road, Edinburgh EH9 3JZ
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Abstract

A special Pisot number is a Pisot number α such that α/(α−1) is also a Pisot number. Lagarias, Porta and Stolarsky found 11 special Pisot numbers. Here it is proved that there are no more. Also, the one known Salem number τ with the property that τ/(τ−1) is a Pisot number is shown to be the only such number.

Type
Notes and Papers
Information
Bulletin of the London Mathematical Society , Volume 31 , Issue 1 , January 1999 , pp. 1 - 5
Copyright
© The London Mathematical Society 1999

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