**
Below is the ascii version of the abstract for 97-474.
The html version should be ready soon.**Knauf, A.
The Number-Theoretical Spin Chain and the Riemann Zeroes
(1021K, Postscript)
ABSTRACT. It is an empirical observation that the Riemann zeta function can be
well approximated in its critical strip using the Number-Theoretical
Spin Chain. A proof of this would imply the Riemann Hypothesis.
Here we relate that question to the one of spectral radii of a family
of Markov chains. This in turn
leads to the question whether certain graphs are Ramanujan.
The general idea is to explain the pseudorandom features of certain
number-theoretical functions by considering them as observables of a
spin chain of statistical mechanics.
In an Appendix we relate the free energy of that chain to the Lewis Equation
of modular theory.