KnowraDirichlet's theorem on arithmetic progressionsLinked fromLinked fromThe 18 pages that link to Dirichlet's theorem on arithmetic progressions, each with the reason it gives.All 18Broader topic 3Related 9Narrower topic 2Compared with 4Dirichlet 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.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.Siegel–Walfisz theoremRelated: It supplies the qualitative existence result that the Siegel–Walfisz theorem sharpens quantitatively.Bunyakovsky conjectureRelated: It proves the Bunyakovsky prediction for linear polynomials.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.