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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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.
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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