The De Bruijn-Newman constant $\Lambda$ was defined and upper bounded by $\Lambda \leq 1/2$ in 1950. After 58 years of work, in 2008 this upper bound was finally improved to ... $\Lambda < 1/2$ (a 0% improvement) in a 26-page paper. The best known upper bound is currently $\Lambda \leq 0.22$. The Riemann hypothesis is equivalent to $\Lambda = 0$, so if it's true then we've got quite a ways to go.
tparker
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