7 papers
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…
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…
Integer moments of the derivatives of the Riemann zeta function
Christopher Hughes, Andrew Pearce-Crump
We conjecture the full asymptotic expansion of a product of Riemann zeta functions, evaluated at the non-trivial zeros of the zeta function, with shifts added in each argument. By…
Complex moments of the derivative of the Riemann zeta function
Christopher Hughes, Andrew Pearce-Crump
We conjecture results about the complex moments of the derivative of the Riemann zeta function, evaluated at the non-trivial zeros of the Riemann zeta function. We do this via two…
The second moment of the Riemann zeta function at its local extrema
Christopher Hughes, Solomon Lugmayer, Andrew Pearce-Crump
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^…
Moments of the Riemann zeta function at its local extrema
Andrew Pearce-Crump
Conrey, Ghosh and Gonek studied the first moment of the derivative of the Riemann zeta function evaluated at the non-trivial zeros of the zeta function, resolving a problem known a…