Michaela Cully-Hugill

activity

20192024

collaborators

3 papers

math.NT2024

On the error term in the explicit formula of Riemann-von Mangoldt II

Michaela Cully-Hugill, Daniel R. Johnston

We give an explicit $O (x / T)$ error term for the truncated Riemann--von Mangoldt explicit formula. For large $x$ , this provides a modest improvement over previous work, which we dem…

math.NT2023

Explicit estimates for the Riemann zeta function close to the $1$ -line

Michaela Cully-Hugill, Nicol Leong

We provide explicit upper bounds of the order $lo g t / lo g lo g t$ for $∣ ζ^{'} (s) / ζ (s) ∣$ and $∣1/ ζ (s) ∣$ when $σ$ is close to $1$ . These improve existing bounds for $ζ (s)$ on the $1$ -li…

math.NT2019

Two explicit divisor sums

Michaela Cully-Hugill, Timothy Trudgian

We give explicit bounds on sums of $d (n)^{2}$ and $d_{4} (n)$ , where $d (n)$ is the number of divisors of $n$ and $d_{4} (n)$ is the number of ways of writing $n$ as a product of four numbe…

On the error term in the explicit formula of Riemann-von Mangoldt II

Explicit estimates for the Riemann zeta function close to the 1-line

Two explicit divisor sums

Explicit estimates for the Riemann zeta function close to the $1$ -line