4 citations · 28 across the 48 of their papers we have counts for
4 papers · 1 filter
On Arithmetic Series involving the fractional part function
Alexander E. Patkowski
We present new relationships between the work of H. Davenport and A. I. Popov. A new general formula involving the Von Mangoldt function is presented, as well as a criteria for the…
On some mellin transforms for the Riemann zeta function in the critical strip
Alexander E Patkowski
We offer two new Mellin transform evaluations for the Riemann zeta function in the region Some discussion is offered in the way of evaluating some further Fourier int…
On Popov's formula involving the Von Mangoldt function
Alexander E Patkowski
We offer a generalization of a formula of Popov involving the Von Mangoldt function. Some commentary on its relation to other results in analytic number theory is mentioned as well…
On special Riemann xi function formulae of Hardy involving the digamma function
Alexander E Patkowski
We consider some properties of integrals considered by Hardy and Koshliakov, and which have also been further extended recently by Dixit. We establish a new general integral formul…