Statements (24)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
arithmetical function
|
| gptkbp:alsoKnownAs |
Λ(n)
|
| gptkbp:appearsIn |
explicit formula for θ(x)
explicit formula for π(x) explicit formula for ψ(x) |
| gptkbp:codomain |
real numbers
|
| gptkbp:defines |
Λ(n) = log p if n = p^k for some prime p and integer k ≥ 1, 0 otherwise
|
| gptkbp:domain |
positive integers
|
| gptkbp:field |
number theory
|
| gptkbp:firstDefined |
1895
|
| https://www.w3.org/2000/01/rdf-schema#label |
von Mangoldt function
|
| gptkbp:namedAfter |
Hans von Mangoldt
|
| gptkbp:property |
multiplicative function
non-negative values Λ(n) = 0 unless n is a power of a prime |
| gptkbp:relatedTo |
gptkb:Möbius_function
gptkb:Chebyshev_function gptkb:prime-counting_function |
| gptkbp:usedIn |
gptkb:Riemann_zeta_function
gptkb:prime_number_theorem explicit formula for the Chebyshev function |
| gptkbp:bfsParent |
gptkb:Chebyshev_R
gptkb:Vaughan's_identity |
| gptkbp:bfsLayer |
8
|