Authors: David Brown
According to the Clay Mathematics Institute, “The prime number theorem determines the average distribution of the primes. The Riemann hypothesis tells us about the deviation from the average. Formulated in Riemann's 1859 paper, it asserts that all the 'non-obvious' zeros of the zeta function are complex numbers with real part 1/2.” Furthermore, if you can write out a valid mathematical proof of the Riemann hypothesis and get it published in a refereed mathematical journal then the Clay Mathematics Institute will, after due deliberation, give you a prize of one million U.S. dollars. The Riemann hypothesis has a generalization to Dirichlet L-functions, among others. What might the Riemann hypothesis and medical predictions have in common? Experience suggests that both are difficult. It might be that accurate prediction of outcomes is mathematically and empirically intractable in almost all interesting cases. Stephen Wolfram’s Principle of Computational Equivalence states that “Almost all processes that are not obviously simple can be viewed as computations of equivalent sophistication.” This brief communication offers two conjectures concerning the generalized Riemann hypothesis for Dirichlet L-functions. In addition to medical doctors and number theory, this brief communication makes reference to Abraham Lincoln and a set of dogs with cardinality one.
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[v1] 2015-11-23 14:26:13
[v2] 2015-11-27 05:22:41
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