Distribution of the Riemann zeros represented by the Fermi gas

Shigenori Tanaka

doi:10.1143/jpsj.80.034001

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arXiv · 1010.4829

Distribution of the Riemann zeros represented by the Fermi gas

Shigenori Tanaka

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Abstract

The multiparticle density matrices for degenerate, ideal Fermi gas system in any dimension are calculated. The results are expressed as a determinant form, in which a correlation kernel plays a vital role. Interestingly, the correlation structure of one-dimensional Fermi gas system is essentially equivalent to that observed for the eigenvalue distribution of random unitary matrices, and thus to that conjectured for the distribution of the non-trivial zeros of the Riemann zeta function. Implications of the present findings are discussed briefly.

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Shigenori Tanaka. 2010-10-28. Distribution of the Riemann zeros represented by the Fermi gas. https://doi.org/10.1143/jpsj.80.034001

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