2 citations · 9 across the 14 of their papers we have counts for
16 papers
Even and Odd Integer Values of the Secondary Zeta Function
Artur Kawalec
The secondary zeta function is defined by where runs over the non-trivial zeros of the Riemann zeta function with positive ordin…
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…
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…
The recurrence formulas for primes and non-trivial zeros of the Riemann zeta function
Artur Kawalec
In this article, we explore the Riemann zeta function with a perspective on primes and non-trivial zeros. We develop the Golomb's recurrence formula for the th+1 prime, and assu…
Nested formulas for cosine and inverse cosine functions based on Viète's formula for
Artur Kawalec
In this article, we develop nested representations for cosine and inverse cosine functions, which is a generalization of Viète's formula for . We explore a natural inverse relat…
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…
Prime product formulas for the Riemann zeta function and related identities
Artur Kawalec
In this article, we derive a Euler prime product formula for the magnitude of the Riemann zeta function valid for , as well as similar formulas for valid fo…
The th+1 Prime Number Limit Formulas
Artur Kawalec
A new derivation of Golomb's limit formula for generating the th prime number is presented. The limit formula is derived by extracting from Euler's prime product r…