Home

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 thus links Riemann ζ function to the BlackScholes option valuation model.

And be sure to check out for the Gallery to see a representation of what I believe is the fundamental reason that there are 3 generations of Particles in Physics and if you are into woo would actually constitute the Platonic Realm in a rigorous way by forming the basis on which a rigorous proof of the Yang-Mills mass gap. There are only 3 of those little island things with the reshaped LensRegion on the ends of them vertically corresponding to the 'trivial zeros'. So, not only does this structure of 3 primitive mathematical objects have a relation in size that strongly suggests some scaling into the relative scales of particle masses in the Standard Model of physics, so not only does the pictorial purely geometric evidence which came from rendering these surfaces with advanced computer programs exist, but so does the infinite sequence of 3-dimensional probability measures on R^3 generated by the regions of negative values of the velocity potential (Real part) of the Y function

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 3 instead of 2, 4, or some other number.

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?

See the page on DifferentialGeometry here which has links to some interesting papers archived here for posterity

--Stephen Crowley