The Number-Theoretical Spin Chain and the Riemann Zeroes
- Andreas KnaufAffiliated withMax-Planck-Institute for Mathematics in the Sciences, Inselstr. 22–26, D-04103 Leipzig, Germany.¶E-mail: email@example.com
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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.
- The Number-Theoretical Spin Chain and the Riemann Zeroes
Communications in Mathematical Physics
Volume 196, Issue 3 , pp 703-731
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- Andreas Knauf (A1)
- Author Affiliations
- A1. Max-Planck-Institute for Mathematics in the Sciences, Inselstr. 22–26, D-04103 Leipzig, Germany.¶E-mail: firstname.lastname@example.org, DE