Contents
Introduction 1
0.1 From Riemann zeta function to dynamical zeta functions . . . 1
0.1.1 Riemann zeta function 1
0.1.2 Problems concerning zeta functions 2
0.1.3 Important types of zeta functions 3
0.1.4 Hasse-Weil zeta function 3
0.1.5 Dynamical zeta functions 4
0.2 Dynamical zeta functions and Nielsen fixed point theory . . . 6
0.3 Congruences for Reidemeister numbers 8
0.4 Reidemeister torsion 9
0.5 Table of contents 11
1 Nielsen Fixed Point Theory 14
1.1 History 14
1.2 Lifting classes and fixed point classes 17
1.2.1 The influence of a homotopy 18
1.3 Reidemeister numbers 19
1.3.1 Reidemeister numbers of a continuous map 19
1.3.2 Reidemeister numbers of a group endomorphism . . . . 21
1.4 Nielsen numbers of a continuous map 22
1.4.1 The fixed point index 22
1.4.2 Nielsen numbers 25
1.4.3 The least number of fixed points 26
2 The Reidemeister zeta function 27
2.1 A Convolution Product 27
2.2 Pontryagin Duality 30
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