  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.
