Contributions To The Theory Of Zeta-Functions: The Modular Relation Supremacy, Kanemitsu Shigeru & Tsukada Haruo

Автор: Alexander Felshtyn
Название: Dynamical Zeta Functions, Nielsen Theory and Reidemeister Torsion
ISBN: 0821820907 ISBN-13(EAN): 9780821820902
Издательство: Oxford Academ
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Описание: In the paper we study dynamical zeta functions connected with Nielsen fixed point theory. The study of dynamical zeta functions is part of the theory of dynamical systems, but it is also intimately related to algebraic geometry, number theory, topology and statistical mechanics. The paper consists of four parts. Part I presents a brief account of the Nielsen fixed point theory. Part II deals with dynamical zeta functions connected with Nielsen fixed point theory. Part III is concerned with analogue of Dold congruences for the Reidemeister and Nielsen numbers. In Part IV we explain how dynamical zefunctions give rise to the Reidemeister torsion, a very important topological invariant which has useful applications in knots theory, quantum field theory and dynamical systems.