KnowraDedekind zeta functionLinked fromLinked fromThe 10 pages that link to Dedekind zeta function, each with the reason it gives.All 10Broader topic 2Related 6Compared with 2Riemann zeta functionCompared with: It generalizes the prime-encoding role of ζ(s) from integers to number fields.Dirichlet L-functionCompared with: Its factorization over quadratic fields includes a Dirichlet L-function.Dirichlet seriesBroader topic: It extends the series method from integers to arithmetic in number fields.Euler productBroader topic: Its product is indexed by prime ideals rather than ordinary primes.Dedekind domainRelated: Unique ideal factorization gives its Euler product over prime ideals.Algebraic number fieldRelated: Its analytic behavior reflects the field's primes, class group, and units.Chebotarev density theoremRelated: Its analytic behavior underlies prime-counting estimates in extensions of number fields.DiscriminantRelated: The field discriminant appears in its functional equation and analytic size estimates.Class number formulaRelated: Its development supplied the analytic object whose residue enters the general formula.Birch–Tate conjectureRelated: The conjecture extracts arithmetic information from its value at zero.