On a solution to a functional equation

We offer a solution to a functional equation using properties of the Mellin transform. A new criteria for the Riemann Hypothesis is offered as an application of our main result, through a functional relationship with the Riemann xi function

A Strange Partition Theorem Related to the Second Atkin-Garvan Moment

This paper contain results on a strange smallest parts function related to the second Atkin-Garvan moment. Some new identities are discovered in relation to Andrews $spt$ function as well as one of Borweins' two-dimensional theta functions.Comment: Final version accepted at International Journal of Number Theor

On Some Families of Integrals Connected to the Hurwitz Zeta Function

Expressions for a family of integrals involving the Hurwitz zeta function are established using standard properties of the Fourier transform

On Arithmetic Series involving the fractional part function

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 Riemann Hypothesis