Memoirs of the American Mathematical Society 2000; 146 pp; softcover Volume: 147 ISBN10: 0821820907 ISBN13: 9780821820902 List Price: US$57 Individual Members: US$34.20 Institutional Members: US$45.60 Order Code: MEMO/147/699
 In the paper we study new 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 analog of Dold congruences for the Reidemeister and Nielsen numbers. In Part IV we explain how dynamical zeta functions give rise to the Reidemeister torsion, a very important topological invariant which has useful applications in knots theory,quantum field theory and dynamical systems. Readership Graduate students and research mathematicians interested in global analysis, analysis on manifolds. Table of Contents  Introduction
 Nielsen fixed point theory
 The Reidemeister zeta function
 The Nielsen zeta function
 Reidemeister and Nielsen zeta functions modulo normal subgroup, minimal dynamical zeta functions
 Congruences for Reidemeister and Nielsen numbers
 The Reidemeister torsion
