DIRICHLET SERIES FOR FINITE COMBINATORIAL RANK DYNAMICS
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY(2010)
摘要
We introduce a class of group endomorphisms - those of finite combinatorial rank - exhibiting slow orbit growth. An associated Dirichlet series is used to obtain an exact orbit counting formula, and in the connected case this series is shown to to be a rational function of exponential variables. Analytic properties of the Dirichlet series are related to orbit-growth asymptotics: depending on the location of the abscissa of convergence and the degree of the pole there, various orbit-growth asymptotics are found, all of which are polynomially bounded.
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关键词
number theory,mathematics,dynamic system,dirichlet series
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