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Twin prime correlations from the pair correlation of Riemann zeros. (English) Zbl 1525.11089

In the paper under review, the authors give an heuristic argument about the equivalence of the Hardy-Littlewood twin prime conjecture and a suitable asymptotic formula for the two-point pair-correlation function for the zeros of the Riemann zeta-function at a height \(E\) on the critical line. The computations rely on unproved conjectures and do not attempt to estimate the errors associated with various approximations. Therefore, it is not clear at the moment whether the connections between the two various conjectures can be transformed into a proof.

MSC:

11M26 Nonreal zeros of \(\zeta (s)\) and \(L(s, \chi)\); Riemann and other hypotheses
11N05 Distribution of primes
15B52 Random matrices (algebraic aspects)
81Q50 Quantum chaos
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