Saturday, December 19, 2020

[fzmrfkok] T-shirt of Watson the number theorist

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89,... I don't understand.

(1/2 + 14.1i), (1/2 + 21.0i), (1/2 + 25.01i), (1/2 + 30.4i), (1/2 + 32.9i), (1/2 + 37.6i), (1/2 + 40.9i), (1/2 + 43.3i), (1/2 + 48.0i), (1/2 + 49.8i), (1/2 + 53.0i), (1/2 + 56.4i), (1/2 + 59.3i), (1/2 + 60.8i), (1/2 + 65.1i), (1/2 + 67.1i), (1/2 + 69.546i), (1/2 + 72.1i), (1/2 + 75.7i), (1/2 + 77.1i), (1/2 + 79.3i), (1/2 + 82.9i), (1/2 + 84.7i), (1/2 + 87.4i),... I still don't understand.

(data from http://www.plouffe.fr/simon/constants/zeta100.html)

Incidentally, the primes become less dense logarithmically while the zeros of the Riemann zeta function become more dense logarithmically.  (Previously.)  (Both exhibit "random" deviations from their statistical trends.)  Can this duality be illustrated elegantly?  Probably Chebyshev psi.  Crossover happens at the 24th terms, at the end of the lists above.

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