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There are Only Eleven Special Pisot Numbers
Author(s) -
Smyth C. J.
Publication year - 1999
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609398005141
Subject(s) - mathematics , mathematics subject classification , combinatorics
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. 1991 Mathematics Subject Classification 11R06.