Mertens' theorem for toral automorphisms

Sawian Jaidee; Shaun Stevens; Thomas Ward

doi:10.1090/S0002-9939-2010-10632-9

Mertens' theorem for toral automorphisms

Sawian Jaidee, Shaun Stevens, Thomas Ward

Algebra and Combinatorics

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

25 Downloads (Pure)

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.

Original language	English
Pages (from-to)	1819-1824
Number of pages	6
Journal	Proceedings of the American Mathematical Society
Volume	139
Issue number	5
DOIs	https://doi.org/10.1090/S0002-9939-2010-10632-9
Publication status	Published - Jan 2011

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10.1090/S0002-9939-2010-10632-9

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http://arxiv.org/abs/0801.2082

Cite this

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title = "Mertens' theorem for toral automorphisms",

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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