Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:convergesTo |
Re(s) > 1
|
| gptkbp:defines |
P(s) = sum over all primes p of 1/p^s
|
| gptkbp:divergesFor |
Re(s) ≤ 1
|
| gptkbp:domain |
Re(s) > 1
|
| gptkbp:field |
gptkb:Number_theory
|
| gptkbp:hasNoEulerProduct |
true
|
| gptkbp:hasSingularityAt |
s = 1
|
| gptkbp:hasSpecialCase |
gptkb:Generalized_zeta_function
|
| https://www.w3.org/2000/01/rdf-schema#label |
Prime zeta function
|
| gptkbp:introduced |
gptkb:Leonhard_Euler
|
| gptkbp:isDirichletSeries |
true
|
| gptkbp:isNotAnalyticContinuation |
true
|
| gptkbp:isNotMultiplicative |
true
|
| gptkbp:relatedTo |
gptkb:Möbius_function
gptkb:Prime_number_theorem gptkb:Riemann_zeta_function gptkb:Euler_product |
| gptkbp:seriesExpansion |
P(s) = sum_{p prime} 1/p^s
|
| gptkbp:symbol |
P(s)
|
| gptkbp:usedIn |
gptkb:Analytic_number_theory
|
| gptkbp:bfsParent |
gptkb:lion
|
| gptkbp:bfsLayer |
4
|