13 citations · 24 across the 8 of their papers we have counts for
8 papers
On the error term in the explicit formula of Riemann-von Mangoldt II
Michaela Cully-Hugill, Daniel R. Johnston
We give an explicit error term for the truncated Riemann--von Mangoldt explicit formula. For large , this provides a modest improvement over previous work, which we dem…
Explicit estimates for the Riemann zeta function close to the -line
Michaela Cully-Hugill, Nicol Leong
We provide explicit upper bounds of the order for and when is close to . These improve existing bounds for on the -li…
An explicit mean-value estimate for the PNT in intervals
Michaela Cully-Hugill, Adrian W. Dudek
This paper gives an explicit version of Selberg's 1943 mean-value estimate for the prime number theorem in intervals under the Riemann hypothesis. Two applications are given: for p…
On the error term in the explicit formula of Riemann--von Mangoldt
Michaela Cully-Hugill, Daniel R. Johnston
We provide an explicit error term for the Riemann--von Mangoldt formula by making results of Wolke (1983) and Ramaré (2016) explicit. We also include applications to…
Primes between consecutive powers
Michaela Cully-Hugill
This paper updates the explicit interval estimate for primes between consecutive powers. It is shown that there is least one prime between and for all $n\ge…
Explicit Interval Estimates for Prime Numbers
Michaela Cully-Hugill, Ethan S. Lee
Using a smoothing function and recent knowledge on the zeros of the Riemann zeta-function, we compute pairs of such that for all there exists at least one pr…
Two explicit divisor sums
Michaela Cully-Hugill, Timothy Trudgian
We give explicit bounds on sums of and , where is the number of divisors of and is the number of ways of writing as a product of four numbe…
A Conditional Explicit Result for the Prime Number Theorem in Short Intervals
Michaela Cully-Hugill, Adrian W. Dudek
We furnish an explicit bound for the prime number theorem in short intervals on the assumption of the Riemann hypothesis.