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Asymptotic Expansions of Some Series Involving the Riemann Zeta Function
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HARDY and Littlewood (stimulated by a conjecture of Ramanujan) proved that the truth of
Σ (-l)nXn/n! Z(2n+1) = 0(X-i+∈)
(∈ > 0 arbitrary) is a necessary and sufficient condition for the truth of the Riemann hypothesis. Here Z(s) is Riemann's Zeta Function.
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