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 | References | Similar Articles | Additional Information

Abstract: A dynamical Mertens' theorem for ergodic toral automorphisms with error term 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:
https://doi.org/10.1090/S0002-9939-2010-10632-9

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.