Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:alsoKnownAs |
gptkb:Riemann_zeta_function
|
| gptkbp:appearsIn |
gptkb:prime_number_theorem
|
| gptkbp:centralTo |
gptkb:Riemann_Hypothesis
|
| gptkbp:domain |
complex numbers
|
| gptkbp:form |
ζ(s) = ∑_{n=1}^∞ 1/n^s
|
| gptkbp:generalizes |
gptkb:lion
gptkb:Hurwitz_zeta_function |
| gptkbp:hasEquation |
ζ(s) = 2^s π^{s-1} sin(πs/2) Γ(1-s) ζ(1-s)
|
| gptkbp:hasSeriesExpansion |
ζ(s) = 1 + 1/2^s + 1/3^s + ...
|
| gptkbp:hasZeros |
trivial zeros at negative even integers
nontrivial zeros in critical strip |
| https://www.w3.org/2000/01/rdf-schema#label |
Euler Z
|
| gptkbp:namedAfter |
gptkb:Leonhard_Euler
|
| gptkbp:relatedTo |
gptkb:Bernhard_Riemann
|
| gptkbp:specialValueAt |
ζ(-1) = -1/12
ζ(0) = -1/2 ζ(2) = π^2/6 ζ(1) diverges |
| gptkbp:usedIn |
complex analysis
number theory |
| gptkbp:bfsParent |
gptkb:crater_Euler
|
| gptkbp:bfsLayer |
7
|