Displaying similar documents to “The Reidemeister zeta function and the computation of the Nielsen zeta function”

A note on dynamical zeta functions for S-unimodal maps

Gerhard Keller (2000)

Colloquium Mathematicae

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Let f be a nonrenormalizable S-unimodal map. We prove that f is a Collet-Eckmann map if its dynamical zeta function looks like that of a uniformly hyperbolic map.

Artin formalism for Selberg zeta functions of co-finite Kleinian groups

Eliot Brenner, Florin Spinu (2009)

Journal de Théorie des Nombres de Bordeaux

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Let Γ ∖ ℍ 3 be a finite-volume quotient of the upper-half space, where Γ ⊂ SL ( 2 , ℂ ) is a discrete subgroup. To a finite dimensional unitary representation χ of Γ one associates the Selberg zeta function Z ( s ; Γ ; χ ) . In this paper we prove the Artin formalism for the Selberg zeta function. Namely, if Γ ˜ is a finite index group extension of Γ in SL ( 2 , ℂ ) , and π = Ind Γ Γ ˜ χ is the induced representation, then Z ( s ; Γ ; χ ) = Z ( s ; Γ ˜ ; π ) . In the second part of the paper we prove by a direct method the analogous identity for the scattering function, namely φ ( s ; Γ ; χ ) = φ ( s ; Γ ˜ ; π ) ,...

The semi-index product formula

Jerzy Jezierski (1992)

Fundamenta Mathematicae

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We consider fibre bundle maps (...) where all spaces involved are smooth closed manifolds (with no orientability assumption). We find a necessary and sufficient condition for the formula    |ind|(f,g:A) = |ind| (f̅,g̅: p(A)) |ind| ( f b , g b : p - 1 ( b ) ∩ A ) to hold, where A stands for a Nielsen class of (f,g), b ∈ p(A) and |ind| denotes the coincidence semi-index from [DJ]. This formula enables us to derive a relation between the Nielsen numbers N(f,g), N(f̅,g̅) and N ( f b , g b ) .