The second moment of the Riemann zeta function at its local extrema

Christopher Hughes; Solomon Lugmayer; Andrew Pearce-Crump

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arXiv · 2411.05573

The second moment of the Riemann zeta function at its local extrema

Christopher Hughes·Solomon Lugmayer·Andrew Pearce-Crump

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Abstract

Conrey and Ghosh studied the second moment of the Riemann zeta function, evaluated at its local extrema along the critical line, finding the leading order behaviour to be $\frac{e^2 - 5}{2 \pi} T (\log T)^2$. This problem is closely related to a mixed moment of the Riemann zeta function and its derivative. We present a new approach which will uncover the lower order terms for the second moment as a descending chain of powers of logarithms in the asymptotic expansion.

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Christopher Hughes, Solomon Lugmayer, Andrew Pearce-Crump. 2024-11-08. The second moment of the Riemann zeta function at its local extrema. https://arxiv.org/abs/2411.05573

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