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It is well-known that the Artin-Mazur dynamical zeta function of a hyperbolic or quasi-hyperbolic toral automorphism is a rational function, which can be calculated in terms of the eigenvalues of the corresponding integer matrix. We give an elementary proof of this fact that extends to the case of general toral endomorphisms without change. The result is a closed formula that can be calculated by integer arithmetic only. We also address the functional equation and the relation between the Artin-Mazur and Lefschetz zeta functions. 相似文献
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It is well-known that the Artin-Mazur dynamical zeta function of a hyperbolic or quasi-hyperbolic toral automorphism is a
rational function, which can be calculated in terms of the eigenvalues of the corresponding integer matrix. We give an elementary
proof of this fact that extends to the case of general toral endomorphisms without change. The result is a closed formula
that can be calculated by integer arithmetic only. We also address the functional equation and the relation between the Artin-Mazur
and Lefschetz zeta functions. 相似文献
3.
Let F be a non-Archimedean local field, with the ring of integersoF. Let G = GLN(F), K = GLN (oF), and be a supercuspidal representationof G. We show that there exists a unique irreducible smoothrepresentation of K, such that the restriction to K of a smoothirreducible representation ' of G contains if and only if 'is isomorphic to ° det, where is an unramified quasicharacterof Fx. Moreover, we show that contains with the multiplicity1. As a corollary we obtain a kind of inertial local Langlandscorrespondence. 2000 Mathematics Subject Classification 22E50. 相似文献
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