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Distribution of the Riemann zeros represented by the Fermi gas

Quantum Physics 2014-05-01 v2 Mathematical Physics math.MP

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.

Keywords

Cite

@article{arxiv.1010.4829,
  title  = {Distribution of the Riemann zeros represented by the Fermi gas},
  author = {Shigenori Tanaka},
  journal= {arXiv preprint arXiv:1010.4829},
  year   = {2014}
}

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7 pages