2 citations · 9 across the 14 of their papers we have counts for
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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…
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…
On the series expansion of the secondary zeta function
Artur Kawalec
In article, we explore the secondary zeta function , which is defined as a generalized zeta type of series over imaginary parts of non-trivial zeros of the Riemann zeta funct…
On the series expansion of a square-free zeta series
Artur Kawalec
In this article, we develop a square-free zeta series associated with the Möbius function into a power series, and prove a Stieltjes like formula for these expansion coefficients.…
The inverse Riemann zeta function
Artur Kawalec
In this article, we develop a formula for an inverse Riemann zeta function such that for we have for real and complex domains and . The presented work…
Analytical recurrence formulas for non-trivial zeros of the Riemann zeta function
Artur Kawalec
In this article, we develop four types of analytical recurrence formulas for non-trivial zeros of the Riemann zeta function on critical line assuming (RH). Thus, all non-trivial ze…
On the complex magnitude of Dirichlet beta function
Artur Kawalec
In this article, we derive an expression for the complex magnitude of the Dirichlet beta function represented as a Euler prime product and compare with similar results for t…
Asymptotic formulas for harmonic series in terms of a non-trivial zero on the critical line
Artur Kawalec
In this article, we develop two types of asymptotic formulas for harmonic series in terms of single non-trivial zeros of the Riemann zeta function on the critical line. The series…