From the 1 of 6 linked papers with an AI index.
6 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 $$ \left|\sum_{n\le x}f(n…
Sharp Upper Bounds for Moments of Dedekind Zeta Functions
Benjamin Durkan, Nilmoni Karak, Kamalakshya Mahatab
Assuming the Generalised Riemann Hypothesis, the authors prove conjecturally sharp upper bounds for shifted moments of products of Dedekind zeta functions over arbitrary number fie…
Amplified moments of the Riemann zeta function
Benjamin Durkan, Timothy Page
We establish asymptotic formulae for two-piece amplified second and fourth moments of the Riemann zeta function. As applications, we obtain unconditional effective lower bounds for…
On the Hardy-Ramanujan Theorem
Benjamin Durkan
In this note we prove an effective version of the Hardy--Ramanujan Theorem. For every and every non-negative function on the non-negative integers, we show $$\frac{1}{…
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…