Volume 11, 2005, Number 1

In this paper we study that the q-Bernoulli polynomial, which were constructed by T. Kim, are analytic continued to β_s(z). A new formula for the q-Riemann Zeta function ζ_q(s) due to T. Kim (see [1,2,8]) in terms of nested series of ζ_q(n) is derived. The new concept of dynamics of the zeros of analytic continued polynomials is introduced, and an investing phenomenon of “scattering” of the zeros of β_s(z) is observed. Following the idea of q-zeta function due to T. Kim, we are going to use “Mathematica” to explore a formula for ζ_q(n).

Prime grids are set up in the Modular Ring Z₆ for the Classes ̅2₆ and ̅4₆. The regular formation of composites intrudes into the grid in a predictable manner, which indicates that the primes form in a structures rather than a haphazard manner when viewed in this way.