A sharpening of Li's criterion for the Riemann Hypothesis

Details A sharpening of Li's criterion for the Riemann Hypothesis A sharpening of Li's criterion for the Riemann Hypothesis

2004-04-10

arxiv.org/abs/math/0404213v2

Mathematics

Number Theory

1 Latex file, 5 pages, submitted to C.R. Acad. Sci. (Paris) S\'er. I. V2: notation corrected in eq.(7); eq.(9) made more preci

Scientific paper

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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