10 papers
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 Berndt's summation formula
Alexander E. Patkowski
We offer a proof of a summation formula equivalent to one due to Berndt. Our proof uses the Mntz formula and the Poisson summation formula. By utilizing known properties…
A note on the -fold Bailey Lemma and Mixed Mock Modular forms
Alexander E. Patkowski
In this paper we present a method for constructing multiple-sum -series for what is known as Mixed Mock Modular forms. We also present some multi-sum analogues of the Durfee ide…
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 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…