A sharpening of Li's criterion for the Riemann Hypothesis
Abstract
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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 April 2004
 arXiv:
 arXiv:math/0404213
 Bibcode:
 2004math......4213V
 Keywords:

 Mathematics  Number Theory;
 Mathematics  Complex Variables;
 11M26 (primary) 30B40;
 41A60 (secondary)
 EPrint:
 1 Latex file, 5 pages, submitted to C.R. Acad. Sci. (Paris) S\'er. I. V2: notation corrected in eq.(7)