The inequality log g(n) < li^{-1}(n) for all n > 0 is equivalent to the Riemann hypothesis.
Barkley Rosser and Lowell Schoenfeld, Approximate f ormulas for some functions of prime numbers, Illinois J
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The Landau function and the Riemann Hypothesis
The inequality log g(n) < li^{-1}(n) for all n > 0 is equivalent to the Riemann hypothesis.