5 citations · 5 across the 4 of their papers we have counts for
11 papers
A sharp almost sure upper bound for partial sums of random multiplicative functions
Benjamin Durkan, Andrew Pearce-Crump
We prove that, for either a Steinhaus random multiplicative function or a Rademacher random multiplicative function , and every $\eps>0$, almost surely $$ \left|\sum_{n\le x}f(n…
Negative discrete second moments of Dirichlet -functions
Andrew Pearce-Crump
Let be a primitive Dirichlet character modulo . Assuming the Generalised Riemann Hypothesis for and that the non-trivial zeros of ar…
A note on a conjecture of Ng
Andrew Pearce-Crump
In this note we give a lower bound for the second moment of a ratio of zeta functions summed over the non-trivial zeros of the Riemann zeta function that is half the size of the co…
A discrete mean-value theorem for the higher derivatives of the Riemann zeta function
Christopher Hughes, Andrew Pearce-Crump
We show that the th derivative of the Riemann zeta function, when summed over the non-trivial zeros of zeta, is real and positive/negative in the mean for odd/even, respecti…
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…
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…