# 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} }

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

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Variants of the Riemann zeta function

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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 of… Expand

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