6 papers
An explicit upper bound for when is quadratic
D. R. Johnston, O. Ramare, T. S. Trudgian
We consider Dirichlet -functions where is a non-principal quadratic character to the modulus . We make explicit a result due to Pintz and Stephens by showing th…
Some explicit results on the sum of a prime and an almost prime
Daniel R. Johnston, Valeriia V. Starichkova
Inspired by a classical result of Rényi, we prove that every even integer can be written as the sum of a prime and a number with at most 395 prime factors. We also show,…
Some explicit estimates for the error term in the prime number theorem
Daniel R. Johnston, Andrew Yang
By combining and improving recent techniques and results, we provide explicit estimates for the error terms , and appearing in the prime…
Exact formulae and Turán inequalities for Vafa-Witten invariants of surfaces
Daniel R. Johnston, Joshua Males
We consider three different families of Vafa-Witten invariants of surfaces. In each case, the partition function that encodes the Vafa-Witten invariants is given by combinatio…
On the average value of
Daniel R. Johnston
We prove that the Riemann hypothesis is equivalent to the condition for all . Here, is the prime-counting functi…
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…