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A lattice gas of prime numbers and the Riemann Hypothesis

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  • Vericat, Fernando

Abstract

In recent years, there has been some interest in applying ideas and methods taken from Physics in order to approach several challenging mathematical problems, particularly the Riemann Hypothesis. Most of these kinds of contributions are suggested by some quantum statistical physics problems or by questions originated in chaos theory. In this article, we show that the real part of the non-trivial zeros of the Riemann zeta function extremizes the grand potential corresponding to a simple model of one-dimensional classical lattice gas, the critical point being located at 1/2 as the Riemann Hypothesis claims.

Suggested Citation

  • Vericat, Fernando, 2013. "A lattice gas of prime numbers and the Riemann Hypothesis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(19), pages 4516-4522.
    • Handle: RePEc:eee:phsmap:v:392:y:2013:i:19:p:4516-4522
    DOI: 10.1016/j.physa.2013.05.049
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