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Perron units which are not Mahler measures

Published online by Cambridge University Press:  19 September 2008

David W. Boyd
David W. Boyd
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, B.C., V6T 1Y4, Canada
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Abstract

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The Mahler measure M(α) of an algebraic integer α is the product of the absolute value of the conjugates of α which lie outside the unit circle. The quantity log M(α) occurs in ergodic theory as the entropy of an endomorphism of the torus. Adler and Marcus showed that if β = M(α) then β is a Perron number which is a unit if α is a unit. They asked whether the Perron number β whose minimal polynomial is tm −t −1 is the measure of any algebraic integer. We show here that the answer is negative for all m > 3.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 6 , Issue 4 , December 1986 , pp. 485 - 488
Copyright
Copyright © Cambridge University Press 1986

References

REFERENCES

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