  Exact and asymptotic formulae are displayed for the coefficients $\lambda_n$
used in Li's criterion for the Riemann Hypothesis. For $n \to \infty$ we obtain
that if (and only if) the Hypothesis is true, $\lambda_n \sim n(A \log n +B)$
(with $A>0$ and $B$ explicitly given, also for the case of more general zeta or
$L$-functions); whereas in the opposite case, $\lambda_n$ has a non-tempered
oscillatory form.
