Riemann conjecture

Cantor strings (or Cantor harps) are one-dimensional drums with a Cantor set as a fractal boundary. They have been studied extensively and an important relationship to the Riemann conjecture was shown [6]. Cantor chains are their discrete counterpart, introduced by the author in [7],... 

It can be shown that, under the assumption that Riemann s conjecture holds, the staircase function of Riemann zeros is given to leading order by (Whittaker and Watson (1927))... 

If one wants a deterministically polynomial-time algorithm that only outputs prime numbers, and where the corresponding factoring assumption follows from that made above, one has to rely on Cramer s conjecture (see above) and search for each prime from some random number upwards in steps of two, and test each number with the pure Miller primality test [Mill76], which relies on the extended Riemann hypothesis. 

Abstract The multiparticle distribution functions and density matrices for ideal Fermi gas system in the ground state are calculated for any spatial dimension. The results are expressed as determinant forms, in which a correlation kernel plays a vital role. The expression obtained for the one-dimensional Fermi gas 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. Their implications are discussed briefly. 

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