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@article{faucris.110638704,
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.},
author = {Knauf, Andreas},
doi = {10.1007/s002200050441},
faupublication = {no},
journal = {Communications in Mathematical Physics},
note = {UnivIS-Import:2015-03-05:Pub.1998.nat.dma.lma6.thenum},
pages = {703-731},
peerreviewed = {Yes},
title = {{The} {Number}-{Theoretical} {Spin} {Chain} and the {Riemann} {Zeroes}},
volume = {196},
year = {1998}
}