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math.NT2026
Generalisations of the Landau--Gonek Theorem and applications to mean values of zeta
Benjamin Durkan, Christopher Hughes, Andrew Pearce-Crump
The Landau--Gonek Theorem evaluates summed over the non-trivial zeros of the Riemann zeta function. Their result shows great sensitivity to the arithmetic nature of . We p…
math.NT2026
The discrete second moment of mixed derivatives of the Riemann zeta function
Benjamin Durkan, Christopher Hughes, Andrew Pearce-Crump
We establish the full asymptotic for the discrete second moment of the Riemann zeta function of mixed derivatives evaluated at the zeta zeros, providing both unconditional and cond…