Source / pinned edition
Li's criterion
Source of package li.positivity_criterion · en.wikipedia.org/wiki/Li_criterion
- work
- urn:doctrine:math:li-positivity-criterion#LI_CRITERION_WIKIPEDIA
- number
- en.wikipedia.org/wiki/Li_criterion
- kind
- urn:doctrine:math:li-positivity-criterion#treatise
LI_CRITERION_WIKIPEDIA_SNAPSHOT
- edition
- urn:doctrine:math:li-positivity-criterion#LI_CRITERION_WIKIPEDIA_SNAPSHOT
- language
- en
- officiality
- unofficial
- materialisation
- PINNED_UNOFFICIAL_COPY
- life cycle
- —
Publications
| URI | Type | documentHash | Retrieved |
|---|---|---|---|
| https://en.wikipedia.org/wiki/Li%27s_criterion | text/plain; charset=utf-8 | sha256:e6b63e1d0b67573e02fb9f27991d32169ecaaf3ec512f107cda17af34cc0f1c0 | 2026-09-17T00:00:00Z |
Fragments — 4
citation · defn · referenced by: 1
en · unofficial · sha256:f4065792582c17df3a56a7113db40424050e77319d8d214952460c38b0f73d03
Li, Xian-Jin (1997). "The positivity of a sequence of numbers and the Riemann hypothesis." Journal of Number Theory 65(2): 325-333. DOI: 10.1006/jnth.1997.2137.Referencing norms: WikipediaSource
definition · defn
en · unofficial · sha256:7d0c8b6ff0bb4f54ad8e3617baed3c337cfc361a1a1c65749845163c42a690ff
Li's criterion. The Li coefficients are defined by
lambda_n = (1/(n-1)!) d^n/ds^n [ s^(n-1) log xi(s) ] evaluated at s = 1,
and equivalently by
lambda_n = sum over rho of [ 1 - (1 - 1/rho)^n ],
where the sum is over the non-trivial zeros rho of the Riemann zeta function, and xi is the Riemann xi function.generalization · defn · referenced by: 4
en · unofficial · sha256:055d29c3a48688f46a3f0e71997795f38ee59cfa7fed43a45ac305fb571c63b8
In 1999, Enrico Bombieri and Jeffrey C. Lagarias provided a generalization demonstrating that Li's positivity condition applies to any collection of points on the Re(s) = 1/2 axis.Referencing norms: BombieriLagariasGeneralization, bl-generalizes-li, generalization-asserted, generalizes
criterion · lemma · referenced by: 3
en · unofficial · sha256:928e81a97e49d2f6882b5432394f4e3a16289f728513780b817df085bfbf9085
Li's criterion states: the Riemann hypothesis is equivalent to the statement that lambda_n > 0 for every positive integer n.Referencing norms: LiCriterionForRiemannZeta, li-asserted-via-wikipedia, li-equivalent-to-rh
The hash beside the text is the sha256 of its exact bytes. It is the check that the text shown matches the one pinned in the package: a divergence fails the oracle’s static analysis.