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arXiv · 0801.2082

Mertens' theorem for toral automorphisms

S. Jaidee·S. Stevens·T. Ward
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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.

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S. Jaidee, S. Stevens, T. Ward. 2008-01-14. Mertens' theorem for toral automorphisms. https://doi.org/10.1090/s0002-9939-2010-10632-9

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