5 papers · 1 filter
On summatory arithmetic functions and a Volterra Integral equation
Alexander E Patkowski
We obtain asymptotic results for well known summatory arithmetic functions, such as and establish connections to new summatory functions. A new Volterra integral equation i…
A general double sum identity, mock theta functions, and Bailey pairs
Alexander E Patkowski
We obtain some Bailey pairs associated with indefinite quadratic forms with the connected to a finite sum. A new general identity is given, which provides identities for -…
A partition identity connected to the second rank moment
Alexander E Patkowski
The purpose of this note is to offer some partition implications of a -series that is connected to the second Atkin-Garvan moment. Inequalities and relationships among the numbe…
On criteria related to the reciprocal of the Riemann zeta function
Alexander E Patkowski
We explore Fourier transforms of the reciprocal of the Riemann zeta function that have connections to the RH. A partial answer to a recently posed problem is explored by exploiting…
Partitions related to positive definite binary quadratic forms
Alexander E Patkowski
The purpose of this paper is to present a collection of interesting generating functions for partitions which have connections to positive definite binary quadratic forms. In estab…