7 papers
Central non-vanishing of Dirichlet -functions
Benjamin Durkan, Andrew Pearce-Crump
We prove that, for every sufficiently large modulus , at least of the primitive Dirichlet characters modulo have . We also esta…
Sharp lower bounds for shifted moments of Dedekind zeta functions
Benjamin Durkan, Nilmoni Karak, Kamalakshya Mahatab
Let be fixed number fields, and let be the compositum of their Galois closures. Assuming GRH for , we prove a sharp lower bound for products of shifted De…
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, we establish conjecturally sharp upper bounds for shifted moments of products of Dedekind zeta functions of arbitrary number fields. Th…
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…
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…