5 papers
On the series expansion of the secondary zeta function about and its coefficients
Artur Kawalec
The secondary zeta function is defined as a generalized zeta series over the imaginary parts of non-trivial zeros assuming (RH). This function admits Laurent series expansion at th…
Analytical continuation of Euler prime product for assuming (RH)
Artur Kawalec
We analytically continue the Euler prime product for (except for its pole ) assuming (RH) by introducing a new factor to the Euler product. We also discu…
Analytical continuation of prime zeta function for assuming (RH)
Artur Kawalec
We derive a simple expression to analytically continue the prime zeta function to the domain assuming (RH) and taking into account a proper branch cut. We also…
On the series expansion of k-free Dirichlet series and its analytical continuation
Artur Kawalec
In this article, we develop a k-free zeta Dirichlet series into a Laurent series with a simple pole, and prove a Stieltjes like formula for the expansion coefficients of the regula…
On the series expansion of the prime zeta function about and its coefficients
Artur Kawalec
In this article, we derive a series expansion of the prime zeta function about the logarithmic singularity and prove general formula for its expansion coefficients, which is…