Sharpenings of Li's Criterion for the Riemann Hypothesis

By André Voros. 2004

48 citations recorded by the source corpus.

Exact and asymptotic formulae are displayed for the coefficients λn used in Li's criterion for the Riemann Hypothesis. For n → ∞ we obtain that if (and only if) the Hypothesis is true, λn ∼ 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, λn has a non-tempered oscillatory form.

Subfields: Algebra and Number Theory, Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/aa6c757d7fbbaecdb766584d6fbc648d940d643c