Partial sum trend growth rates of the positive and negative components of the Real and Imaginary parts of finite Dirichlet Series

John Martin
2022 figshare.com  
As the number of terms, in the finite Riemann Zeta Dirichlet series exceed N = t·Nc/π where t is the imaginary component of a point in the complex plane (away from the real axis) and Nc is the conductor value of the Riemann Zeta function, the leading trend term of the growth rates of the 4 separate partial sums respectively of the positive and negative components of the Real and Imaginary parts of Riemann Zeta Dirichlet Series exhibit an absolute magnitude that can be written as a Box-Cox
more » ... ormation. Such an absolute magnitude of growth of the leading term is similar in magnitude to generous (older) known upper bounds of the magnitude of the Riemann Zeta function growth (|ζ(s)|. This empirical study shows the Box-Cox transformation functional behaviour also extends outside the critical strip and the Mellin transform representation of the Riemann Zeta function as a Dirac comb aids in interpretation of the empirical behaviour.
doi:10.6084/m9.figshare.21151810.v1 fatcat:7rrzi5ftibcerjuv7epzheaohq