KnowraDirichlet characterLinked fromLinked fromThe 10 pages that link to Dirichlet character, each with the reason it gives.All 10Broader topic 5Related 4Narrower topic 1Dirichlet's theorem on arithmetic progressionsBroader topic: Characters modulo the common difference isolate primes in the progression’s residue class.Dirichlet L-functionBroader topic: Its values supply the coefficients in the defining series and determine each member of the family.Legendre symbolNarrower topic: For fixed prime p, the Legendre symbol is a Dirichlet character modulo p.Multiplicative functionBroader topic: These functions turn congruence conditions into multiplicative coefficients for Dirichlet series.Prime number theorem for arithmetic progressionsRelated: Characters turn prime counts in individual residue classes into sums suited to analytic methods.Bombieri–Vinogradov theoremBroader topic: Character sums transform progression errors into quantities that can be averaged.Linnik's theoremRelated: Character sums turn primes in a residue class into analytic objects that can be estimated.Peter Gustav Lejeune DirichletBroader topic: Dirichlet used these functions to isolate individual arithmetic progressions.Kronecker–Weber theoremRelated: Characters describe abelian subfields of cyclotomic fields through their Galois actions.Siegel–Walfisz theoremRelated: Character sums convert prime counts in individual residue classes into analytic estimates.