The Riemann hypothesis as a margin: a two-sided criterion verified to 2*10^29, the fourth-moment anatomy of Mobius cancellation, and one constant seen from every side
This paper collects, with uniform notation, a month of new results around one way of looking at the Riemann hypothesis (RH): as the statement that explicitly computable margins stay on one side of explicit constants for ever. Part I studies the Cesaro margin M(N) between a smooth curve and the weighted prime sum 2*sum_{q = 0 for all large N (a theorem of Suzuki), and we verify 0 = 2B unconditionally, with equality if and only if RH holds with simple zeros), the energy slope as a truncated Weil functional exact in the primes, the functional reflection that reproduces Hardy's function from the…
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