Correlations of the squares of the Riemann zeta on the critical line

Valeriya Kovaleva

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arXiv · 2401.13725

Correlations of the squares of the Riemann zeta on the critical line

Valeriya Kovaleva

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Abstract

We compute the average of a product of two shifted squares of the Riemann zeta on the critical line with shifts up to size $T^{3/2-\varepsilon}$. We give an explicit expression for such an average and derive an approximate spectral expansion for the error term similar to Motohashi's. As a consequence, we also compute the $(2,2)$-moment of moment of the Riemann zeta, for which we partially verify (and partially refute) a conjecture of Bailey and Keating.

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Valeriya Kovaleva. 2024-01-24. Correlations of the squares of the Riemann zeta on the critical line. https://arxiv.org/abs/2401.13725

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