0.1 From Riemann zeta function to dynamical
zeta functions
In this subsection we shall try to explain where dynamical zeta functions
come from . In a sense 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.
0.1.1 Riemann zeta function
The theory of the Riemann zeta function and its generalisations represent
one of the most beatiful developments in mathematics. The Riemann zeta
function is that function defined on {s G W\ Re(s) 1} by the series
There is a second representation of ( which was discovered by Euler in 1749
and which is the reason for the significance of the Riemann zeta function in
arithmetic. This is Euler product formula:
as)= n
p prime
Received by the editor June 22, 1998
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