A hybrid Euler-Hadamard product for the Riemann zeta function

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Conjectures for the integral moments and ratios of L-functions over function fields (2014, unknown): “The separation into arithmetic and random matrix factors is explained by a hybrid product formula for ζ(s) that includes both the primes and the zeros [21].”
Asymptotics of Toeplitz, Hankel, and Toeplitz+Hankel determinants with Fisher-Hartwig singularities (2009, methodology): “1 were used in the unitary case in [27].”
Sharp conditional bounds for moments of the Riemann zeta function (2013, background): “For example, Gonek, Hughes and Keating [5] showed, roughly speaking, that if the Riemann Hypothesis is true then where p denotes primes, c > 0 is a constant, and the second product is over ordinates γ of zeros of the zeta function.”
The maximum size of L-functions (2005, methodology): “When X is not too large, we expect ZX and PX to behave somewhat independently, and Gonek, Hughes, and Keating [ 8 ] give evidence of this.”