Mertens’ theorem for toral automorphisms
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- by Sawian Jaidee, Shaun Stevens and Thomas Ward PDF
- Proc. Amer. Math. Soc. 139 (2011), 1819-1824 Request permission
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.References
Additional Information
- Sawian Jaidee
- Affiliation: Department of Mathematics, 123 Mittraphab Road, Khon Kaen University 40002, Thailand
- MR Author ID: 772773
- Shaun Stevens
- Affiliation: School of Mathematics, University of East Anglia, Norwich NR4 7TJ, United Kingdom
- MR Author ID: 678092
- Thomas Ward
- Affiliation: School of Mathematics, University of East Anglia, Norwich NR4 7TJ, United Kingdom
- MR Author ID: 180610
- Received by editor(s): May 27, 2010
- Published electronically: November 1, 2010
- Communicated by: Bryna Kra
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 139 (2011), 1819-1824
- MSC (2010): Primary 37C35, 11J72
- DOI: https://doi.org/10.1090/S0002-9939-2010-10632-9
- MathSciNet review: 2763768