prime number theorem for arithmetic progressions
GPTKB entity
Statements (18)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:alsoKnownAs |
gptkb:Dirichlet's_theorem_on_arithmetic_progressions
|
| gptkbp:concerns |
distribution of prime numbers
|
| gptkbp:field |
number theory
|
| gptkbp:generalizes |
gptkb:prime_number_theorem
|
| https://www.w3.org/2000/01/rdf-schema#label |
prime number theorem for arithmetic progressions
|
| gptkbp:implies |
infinitely many primes in every coprime residue class
|
| gptkbp:namedAfter |
gptkb:Peter_Gustav_Lejeune_Dirichlet
|
| gptkbp:provenBy |
gptkb:Hadamard
gptkb:de_la_Vallée-Poussin |
| gptkbp:relatedTo |
gptkb:Dirichlet's_theorem
gptkb:Riemann_hypothesis_for_Dirichlet_L-functions |
| gptkbp:result |
π(x; q, a) ~ li(x)/φ(q) as x→∞ for (a, q)=1
|
| gptkbp:state |
primes are evenly distributed among coprime residue classes
|
| gptkbp:uses |
gptkb:Dirichlet_L-functions
|
| gptkbp:yearProved |
1896
|
| gptkbp:bfsParent |
gptkb:Chebyshev_bias
|
| gptkbp:bfsLayer |
7
|