Tuesday, October 16, 2018

[pszsinsd] Generalized Riemann zeroes everywhere

Associate different Dirichlet L-functions with locations on earth.  In an augmented reality game (inspired by Pokemon Go), prizes appear at a location at times corresponding to zeroes along the critical line for the L-function of that location.  The time at which a zero appears corresponds to its height, the imaginary component of the zero.  We will need to do some scaling so that prizes don't come increasingly frequently as density of zeroes increases with height.

I think we can't associate every point on a sphere with a different L-function because there are only countably infinite L-functions but uncountably infinite points on a sphere.  Also, there would be an infinite number of prizes popping up every moment within any region.

Best would be to subdivide the earth into regions then associate one L-function to each region.

Of course, anyone knowing the mapping can predict in advance when and where prizes will appear, but doing so requires learning about Dirichlet L-functions and the generalized Riemann hypothesis.  Can we instead design it so that predicting prizes actually requires assuming GRH, so that it will be very interesting if a prediction is ever wrong?

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