A sharpening of Li's criterion for the Riemann Hypothesis
Abstract
Description
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.
1 Latex file, 5 pages, submitted to C.R. Acad. Sci. (Paris) Sér. I. V2: notation corrected in eq.(7); eq.(9) made more precise
1 Latex file, 5 pages, submitted to C.R. Acad. Sci. (Paris) Sér. I. V2: notation corrected in eq.(7); eq.(9) made more precise