4 citations · 28 across the 48 of their papers we have counts for
49 papers
On an spt function for the -th symmetrized crank function
Alexander E. Patkowski
In this paper we find the smallest part function related to the -th symmetrized crank function, corresponding to the one obtained in Patkowski [11] for the -th symmetrized ra…
An application of Titchmarsh's theorem and the Salem equivalence
Alexander E. Patkowski
We extend the equivalence of the Salem type for the Riemann hypothesis by application of Titchmarsh's theorem. Other equivalences to the Riemann hypothesis and notes on related Fou…
On certain sums over primes and the Riesz function
Alexander E. Patkowski
We offer some comments on series involving the Mbius function which approximate sums over primes. To accomplish this, we utilize the derivative of the Gram series by appl…
On curious properties of the general size-biased distribution
Alexander E. Patkowski
We offer further results on a general size-biased distribution related to the Riemann xi-function we presented in [9] using the work of Ferrar. Curious properties associated with i…
On a Bessel function series related to the Riemann xi function
Alexander E. Patkowski
We establish new Fourier integral evaluations involving the Riemann xi function related to a series involving Bessel function of the first kind. We show this infinite series involv…
On the harmonic continuation of the Riemann xi function
Alexander E. Patkowski
We generalize the harmonic continuation of the Riemann xi-function to the -dimension case, to obtain the solution to the Dirichlet problem on We also pro…