Mertens' theorem for toral automorphisms

Jaidee, S.; Stevens, S.; Ward, T.

Abstract

A dynamical Mertens' theorem for ergodic toral automorphisms with error term 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.

Citation

Jaidee, S., Stevens, S., & Ward, T. (2011). Mertens' theorem for toral automorphisms. Proceedings of the American Mathematical Society, 139(05), 1819-1824. https://doi.org/10.1090/s0002-9939-2010-10632-9

• Journal Article Type: Article
• Publication Date: Jan 1, 2011
• Deposit Date: Oct 12, 2012
• Publicly Available Date: Dec 14, 2012
• Journal: Proceedings of the American Mathematical Society
• Print ISSN: 0002-9939
• Electronic ISSN: 1088-6826
• Publisher: American Mathematical Society
• Peer Reviewed: Peer Reviewed
• Volume: 139
• Issue: 05
• Pages: 1819-1824
• DOI: https://doi.org/10.1090/s0002-9939-2010-10632-9
• Public URL: https://durham-repository.worktribe.com/output/1473187