Corpus ID: 119619212

# Experiments with the dynamics of the Riemann zeta function

```@inproceedings{Brent2017ExperimentsWT,
title={Experiments with the dynamics of the Riemann zeta function},
author={B. Brent},
year={2017}
}```
• B. Brent
• Published 26 March 2017
• Mathematics
We collect experimental evidence for several propositions, including the following: (1) For each Riemann zero ρ (trivial or nontrivial) and each zeta fixed point ψ there is a nearly logarithmic spiral sρ,ψ with center ψ containing ρ. (2) sρ,ψ interpolates a subset Bρ,ψ of the backward zeta orbit of ρ comprising a set of zeros of all iterates of zeta. (3) If zeta is viewed as a function on sets, ζ(Bρ,ψ) = Bρ,ψ ∪ {0}. (4) Bρ,ψ has nearly uniform angular distribution around the center of sρ,ψ. We… Expand
1 Citations

#### Figures from this paper

Variants of the Riemann zeta function
We construct variants of the Riemann zeta function with convenient properties and make conjectures about their dynamics; some of the conjectures are based on an analogy with the dynamical system ofExpand

#### References

SHOWING 1-10 OF 11 REFERENCES
The holomorphic flow of the Riemann zeta function
• Mathematics, Computer Science
• Math. Comput.
• 2004
The flow of the Riemann zeta function, s = ζ(s), is considered, and phase portraits are presented, which suggest new analytic properties of zeta, of which some are proved and others are given in the form of conjectures. Expand
A Dynamical Key to the Riemann Hypothesis
We investigate a dynamical basis for the Riemann hypothesis (RH) that the non-trivial zeros of the Riemann zeta function lie on the critical line x = 1/2. In the process we graphically explore, in asExpand
Fractal Geography of the Riemann Zeta Function
The quadratic Mandelbrot set has been referred to as the most complex and beautiful object in mathematics and the Riemann Zeta function takes the prize for the most complicated and enigmaticExpand
Fractals of the Julia and Mandelbrot sets of the Riemann Zeta Function
Computations of the Julia and Mandelbrot sets of the Riemann zeta function and observations of their properties are made. In the appendix section, a corollary of Voronin's theorem is derived and aExpand
Theory of Functions of a Complex Variable
• Mathematics
• 1968
Volume I, Part 1: Basic Concepts: I.1 Introduction I.2 Complex numbers I.3 Sets and functions. Limits and continuity I.4 Connectedness. Curves and domains I.5. Infinity and stereographic projectionExpand
Dynamics of Transcendental Functions
• Mathematics
• 2019
Let f be a nonconstant meromorphic function. The sequence of the iterates of f is denoted by \$\${f^0}=id,{f^1}=f,\cdots,{f^{n + 1}} = {f^n}(f), \cdots\$\$
Resources, 2017. www.researchgate.net/project/Experimentswith-the-dynamics-of-the-Riemann-zeta-function
• 2017
Dynamics of Transcendental Functions. Gordon and Breach Science Publishers, Australia Canada China France Germany India Japan Luxembourg Malaysia
• The Netherlands Russia Singapore Switzerland,
• 1998
Riemann’s zeta function, newton’s method, and holomorphic index, poster presented at kansuron’s summer seminar
• 1998