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I created arb4j because I needed complex numbers in Java so I could write software to play with functions described in Complex Dynamics of The Hyperbolic Tangent of The Logarithm Of One Minus The Square of The Hardy Z Function and arblib which is something I just did for fun and the heck of it. I first learned of the RiemannZetaFunction when I was studying ProbabilityTheory back in the day trying to figure out how to price and trade options where it turns out that the BrownianBridge has functionals of excursion times related to the Riemann ξ function.

And be sure to check out for the Gallery to see a representation of what I believe could be the very reason that there are 3 generations of Particles in Physics. There are only 3 of those little island things with the reshaped LensRegion on the ends of them vertically corresponding to the 'trivial zeros'.

My prediction is that out those zeros might be trivial as far as their location in the complex plain goes but they are not trivial at all given that they are probably are related to YangMillsTheory as described in Towards non-perturbative quantization and the mass gap problem for the Yang-Mills Field where DrAlexySevastyanov reformulated the Yang-Mills problem as the existence of an infinite set of gauge equivalence classes of connections on R^3 and some other criteria... and is actually the very reason that there are ThreeGenerations of fundamental particles in physics and hitherto it has been a complete mystery as to why nature 'chose' 3 instead of 2, 4, or some other number. As loathe as some are to accept 'pictures' as 'proof', the reason can be seen clearly by looking in the Gallery or running the program yourself to locate your coordinates in this undiscovered continent.

Learn more about it at Wikipedia's page on Gauge 'fixing' and I believe there exists an entirely different 'mechanism' by which particles 'acquire' mass , written by the same guy Mr. Sevastyanov who reformulated the Yang-Mills mass-gap existence question into the form generated by the completion of my work on the Riemann hypothesis and apparently has nothing to do with the 'unobservable Higgs'. I could be wrong about this, but that's my hunch as of now..... were these models actually ruled out by the LHC or were they just forgotten?

--Stephen Crowley