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We refine a recent heuristic developed by Keating and the second author. Ourimprovement leads to a new integral expression for the conjectured asymptoticformula for shifted moments of the Riemann zeta-function. This expression isanalogous to a formula, recently discovered by Brad Rodgers and KannanSoundararajan, for moments of characteristic polynomials of random matricesfrom the unitary group.

Moments of zeta and correlations of divisor-sums: stratification and Vandermonde integrals