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Sharpenings 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. For $n \to \infty$ we obtain that if (and only if) the Hypothesis is true, $λ_n \sim n(A \log n +B)$ (with $A>0$ and $B$ explicitly given, also for the case of more general zeta or $L$-functions); whereas in the opposite case, $λ_n$ has a non-tempered oscillatory form.

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André Voros. 2006-01-25. Sharpenings of Li's criterion for the Riemann Hypothesis. https://doi.org/10.1007/s11040-005-9002-8

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