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A sharpening of Li's criterion for the Riemann Hypothesis

André Voros
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Abstract

Exact and asymptotic formulae are displayed for the coefficients $λ_n$ used in Li's criterion for the Riemann Hypothesis. In particular, we argue that if (and only if) the Hypothesis is true, $λ_n \sim n(A \log n +B)$ for $n \to \infty$ (with explicit $A>0$ and $B$). The approach also holds for more general zeta or $L$-functions.

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André Voros. 2004-04-15. A sharpening of Li's criterion for the Riemann Hypothesis. https://arxiv.org/abs/math/0404213

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