ConvergentNormalisationofOrdinaryDirichletSeriesinLowerHalfofComplexPlane.pdf (1.03 MB)

A normalisation of the ordinary Dirichlet Series in the lower half complex plane that has the equivalent normalised Riemann Zeta function as an detrended envelope function.

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journal contribution
posted on 16.03.2017, 21:59 by John Martin
In the lower half complex plane Re(s)<1, a convergent normalisation of the ordinary dirichlet series is given, with a functional dependence on the real axis of 1/(1-Re(s)). Off the real axis, the normalised series has an upper (lower) detrended envelope function of the form ±| ζ(s)/N^(1−Re(s))|, for 10000 < N < ∞.

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