Linked from

The 18 pages that link to Dirichlet's theorem on arithmetic progressions, each with the reason it gives.

• Analytic number theoryBroader topic: Its proof uses Dirichlet L-functions to show primes recur in each eligible progression.

• Diophantine approximationCompared with: It is a distinct theorem by Dirichlet, unlike his foundational approximation theorem.

• Dirichlet L-functionRelated: Nonvanishing of Dirichlet L-functions at s=1 drives the theorem's proof.

• Euler productRelated: Dirichlet used L-function Euler products to prove primes occur across such progressions.

• Dirichlet characterRelated: Dirichlet characters are the central analytic tool in its proof.

• Prime number theorem for arithmetic progressionsNarrower topic: It guarantees infinitude in each eligible class; this theorem quantifies their distribution.

• Hardy–Littlewood conjecturesRelated: It establishes prime occurrence in individual residue classes, a local ingredient in pattern heuristics.

• Linnik's theoremRelated: It guarantees existence, while Linnik's theorem additionally bounds how early the first prime appears.

• Peter Gustav Lejeune DirichletBroader topic: This landmark result connected prime distribution with Dirichlet’s use of analysis.

• Euclid's theoremBroader topic: It extends infinitude to primes in particular arithmetic progressions.

• Chebotarev density theoremCompared with: It is the abelian arithmetic-progression case that Chebotarev broadly generalizes.

• Sophie Germain primeCompared with: It guarantees primes in simple progressions, but does not establish infinitely many Sophie Germain primes.

• Siegel–Walfisz theoremRelated: It supplies the qualitative existence result that the Siegel–Walfisz theorem sharpens quantitatively.

• Brun–Titchmarsh theoremCompared with: Dirichlet’s theorem guarantees infinitude; Brun–Titchmarsh gives a quantitative upper bound.

• Bunyakovsky conjectureRelated: It proves the Bunyakovsky prediction for linear polynomials.

• Artin's conjecture on primitive rootsNarrower topic: The conjecture's prime conditions lead into counting primes across arithmetic progressions.

• Divergence of the sum of the reciprocals of the primesRelated: Its stronger analytic forms show reciprocal primes also diverge within each eligible progression.

• Schinzel's theoremRelated: It is a classical model for proving that arithmetic conditions hold for infinitely many primes.