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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…
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…
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…