Mathematics – Number Theory
Scientific paper
2005-06-16
Math. Phys. Anal. Geom. 9 (2006) 53-63
Mathematics
Number Theory
10 pages, Math. Phys. Anal. Geom (2006, at press). V2: minor text corrections and updated references
Scientific paper
10.1007/s11040-005-9002-8
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.
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