The holomorphic flow of the Riemann zeta function
| Citations: | 2 - 2 self |
BibTeX
@MISC{Broughan_theholomorphic,
author = {Kevin A. Broughan and A. Ross Barnett},
title = {The holomorphic flow of the Riemann zeta function},
year = {}
}
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Abstract
The flow of the Riemann zeta function, ˙s = ζ(s), is considered and phase portraits presented. Attention is given to the characterization of the flow lines in the neighborhood of the first 500 zeros on the critical line. All of these zeros are foci. The majority are sources, but in a small proportion of exceptional cases, the the zero is a sink. To produce these portraits, the zeta function was evaluated numerically to 12 decimal places, in the region of interest, using the Chebyshev method and using Mathematica. The phase diagrams suggest new analytic properties of zeta, a number of which are proved and a number of which are given in the form of conjectures.
