Below is the ascii version of the abstract for 97-474.
The html version should be ready soon.
The Number-Theoretical Spin Chain and the Riemann Zeroes
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.