The Reidemeister zeta function and the computation of the Nielsen zeta function
A. Fel'shtyn (1991)
Colloquium Mathematicum
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Displaying similar documents to “Dynamical zeta functions, congruences in Nielsen theory and Reidemeister torsion”
The Reidemeister zeta function and the computation of the Nielsen zeta function
Fixed point theory and the K-theoretic trace
Ross Geoghegan, Andrew Nicas (1999)
Banach Center Publications
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The relationship between fixed point theory and K-theory is explained, both classical Nielsen theory (versus ) and 1-parameter fixed point theory (versus ). In particular, various zeta functions associated with suspension flows are shown to come in a natural way as “traces” of “torsions” of Whitehead and Reidemeister type.
A note on functional equations for zeta functions with values in Chow motives
Franziska Heinloth (2007)
Annales de l’institut Fourier
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We consider zeta functions with values in the Grothendieck ring of Chow motives. Investigating the –structure of this ring, we deduce a functional equation for the zeta function of abelian varieties. Furthermore, we show that the property of having a rational zeta function satisfying a functional equation is preserved under products.
Preface, Contents
(1999)
Banach Center Publications
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On analytic torsion over C*-algebras
Alan Carey, Varghese Mathai, Alexander Mishchenko (1999)
Banach Center Publications
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In this paper, we present an analytic definition for the relative torsion for flat C*-algebra bundles over a compact manifold. The advantage of such a relative torsion is that it is defined without any hypotheses on the flat C*-algebra bundle. In the case where the flat C*-algebra bundle is of determinant class, we relate it easily to the L^2 torsion as defined in [7],[5].
An introduction to the abelian Reidemeister torsion of three-dimensional manifolds
Gwénaël Massuyeau (2011)
Annales mathématiques Blaise Pascal
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These notes accompany some lectures given at the autumn school “” in October 2009. The abelian Reidemeister torsion for -manifolds, and its refinements by Turaev, are introduced. Some applications, including relations between the Reidemeister torsion and other classical invariants, are surveyed.
On the zeta functions of prehomogeneous vector spaces for a pair of simple algebras
Takashi Taniguchi (2007)
Annales de l’institut Fourier
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In this paper we consider the prehomogeneous vector space for a pair of simple algebras which are inner forms of the type and the type. We mainly study the non-split cases. The main purpose of this paper is to determine the principal parts of the global zeta functions associated with these spaces when the simple algebras are non-split. We also give a description of the sets of rational orbits of these spaces, which clarifies the expected density theorems arising from the properties...