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Christopher Deninger Some Ideas on Dynamical Systems and the Riemann Zeta Function [PS format] Preprint series: Proceedings of the ESI conference on the Riemann Zeta Function
ads to the investigation of a class of dynamical systems on foliated spaces. The hope is that finding the right dynamical system will be an important step towards a better understanding of $\zeta (s)$. The entire approach carries over to motivic $L$-series the most general kind of $L$-series coming from arithmetic geometry. This is important for various reasons but for simplicity we will mostly be concerned with $\zeta (s)$. In the first section we recall some arguments from \cite{D1} in favour of a possible
cohomological interpretation of the Riemann zeta function. In the second section
following \cite{D2}, \cite{D3} we single out a class of foliated dynamical
systems whose leafwise reduced cohomology has many of the formal properties desired
in section one. We close with a number of further remarks and suggestions.
For other approaches to $\zeta (s)$ via dynamical systems the reader may consult
the works by Berry \cite{B} and Connes \cite{C}.
Keywords: Riemann zeta function, dynamical systems on foliated spaces, leafwise reduced cohomology
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