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A sharpening of Li's criterion for the Riemann Hypothesis

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arxiv math/0404213 v2 pith:TUSNQ2K3 submitted 2004-04-10 math.NT math.CV

André Voros This is my paper · ORCID
classification math.NTmath.CV
keywords hypothesiscriterionlambdariemannapproachargueasymptoticcoefficients
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abstract

Exact and asymptotic formulae are displayed for the coefficients $\lambda_n$ used in Li's criterion for the Riemann Hypothesis. In particular, we argue that if (and only if) the Hypothesis is true, $\lambda_n \sim n(A \log n +B)$ 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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  1. Analysis of a Complex approximation to the Li-Keiper coefficients around the K Function

    math.GM 2019-06 unverdicted novelty 2.0 of 10

    Authors set up a closed system of equations for perturbed Li-Keiper coefficients around the Koebe function and report numerical evidence that fluctuations lambda-tiny(n) remain bounded by gamma times n.

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