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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Mertens' theorem for toral automorphisms


Authors: Sawian Jaidee, Shaun Stevens and Thomas Ward
Journal: Proc. Amer. Math. Soc. 139 (2011), 1819-1824
MSC (2010): Primary 37C35, 11J72
Published electronically: November 1, 2010
MathSciNet review: 2763768
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Abstract: A dynamical Mertens' theorem for ergodic toral automorphisms with error term  $ \operatorname{O}(N^{-1})$ is found, and the influence of resonances among the eigenvalues of unit modulus is examined. Examples are found with many more, and with many fewer, periodic orbits than expected.


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Additional Information

Sawian Jaidee
Affiliation: Department of Mathematics, 123 Mittraphab Road, Khon Kaen University 40002, Thailand

Shaun Stevens
Affiliation: School of Mathematics, University of East Anglia, Norwich NR4 7TJ, United Kingdom

Thomas Ward
Affiliation: School of Mathematics, University of East Anglia, Norwich NR4 7TJ, United Kingdom

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10632-9
PII: S 0002-9939(2010)10632-9
Received by editor(s): May 27, 2010
Published electronically: November 1, 2010
Communicated by: Bryna Kra
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.