Hardy-Littlewood series

Hardy and Littlewood (Acta Mathematica 41 (1918), 119 - 196) showed that the Riemann Hypothesis is equivalent to the estimate

$$\sum_{k=1}^\infty \frac{(-x)^k}{k!\zeta(2k+1)}\ll x^{-1/4}$$

as $x\to \inftu$.

Back to the main index for The Riemann Hypothesis.