Sharpenings 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. 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.

10 pages, Math. Phys. Anal. Geom (2006, at press). V2: minor text corrections and updated references

References in corpus (1)

• Toward verification of the Riemann hypothesis: Application of the Li criterion

Cited by in corpus (4)

• On Differences of Zeta Values
• Discretized Keiper/Li approach to the Riemann Hypothesis
• On certain sums over the nontrivial zeta zeros
• The saddle-point method and the Li coefficients