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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 [D1] in favour of a possible
cohomological interpretation of the Riemann zeta function. In the second section
following [D2], [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 [B] and Connes [C].
Keywords: Riemann zeta function, dynamical systems on foliated spaces, leafwise reduced cohomology
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