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arcs in the Riemann zeta and other Dirichlet L functions
A recent birthday present (my 36th) was Elias Wegert's Visual complex functions. On the sides of the pages are strips -- excerpts from the critical strip of the Riemann zeta function with nontrivial roots. He wrote a paper about the stochastic period of 2$\pi$, which is easily observable in the below image as the yellow diagonals:
He's got the images of the functions up on a functions gallery on the website associated with the book. I thought I couldn't see what was going on so I used the gimp to prune the white regions from the images and to glue the remainders together. So, this led to a mathoverflow question after I asked Matt McIrvin to take a Fourier transform -- which he did with a set discretely supported on the roots of the Riemann zeta function, and a post on the n-category cafe concerning Freeman Dyson's speculation that the roots might form a quasicrystal. There are some obvious questions:

Bounty: I am offering a bottle of whisky to anyone who can successfully translate Jacob Lurie's Higher Topos Theory (and/or the stacks project) into the analytic combinatorical language of the manner of Flajolet's Analytic Combinatorics.