Introduction

      Creation Functions
            DirichletGroup(I) : RngOrdIdl -> GrpDrchNF
            HeckeCharacterGroup(I) : RngOrdIdl -> GrpHecke
            UnitTrivialSubgroup(G) : GrpDrchNF -> GrpDrchNF
            TotallyUnitTrivialSubgroup(G) : GrpDrchNF -> GrpDrchNF
            HilbertCharacterSubgroup(G) : GrpHecke -> GrpHecke

      Functions on Groups and Group Elements
            Modulus(G) : GrpDrchNF -> RngOrdIdl, SeqEnum
            Order(chi) : GrpDrchNFElt -> RngIntElt
            Random(G) : GrpDrchNF -> GrpDrchNFElt
            Domain(G) : GrpDrchNF -> FldNum
            Domain(G) : GrpHecke -> PowIdl
            Decomposition(chi) : GrpDrchNFElt -> List
            Components(chi) : GrpDrchNFElt -> Assoc
            Component(chi, P) : GrpDrchNFElt, RngOrdIdl -> GrpDrchNFEl
            Conductor(chi) : GrpDrchNFElt -> RngOrdIdl, SeqEnum
            AssociatedPrimitiveCharacter(chi) : GrpDrchNFElt -> GrpDrchNFElt
            Restrict(chi, D) : GrpDrchNFElt, GrpDrchNF -> GrpDrchNFElt
            TargetRestriction(G, C) : GrpDrchNF, FldCyc -> GrpDrchNF
            SetTargetRing(~chi, e) : GrpDrchNFElt, RngElt ->
            Extend(chi, D) : GrpDrchNFElt, GrpDrchNF -> GrpDrchNFElt

      Predicates on Group Elements
            IsTrivial(chi) : GrpDrchNFElt -> BoolElt
            IsTrivialOnUnits(chi) : GrpDrchNFElt -> BoolElt
            IsOdd(chi) : GrpDrchNFElt -> BoolElt
            IsEven(chi) : GrpDrchNFElt -> BoolElt
            IsTotallyEven(chi) : GrpDrchNFElt -> BoolElt
            IsPrimitive(chi) : GrpDrchNFElt -> BoolElt

      Passing between Dirichlet and Hecke Characters
            HeckeLift(chi) : GrpDrchNFElt -> GrpHeckeElt, GrpHecke
            DirichletRestriction(psi) : GrpHeckeElt -> GrpDrchNFElt
            NormInduction(K, chi) : FldNum, GrpDrchElt -> GrpHeckeElt
            QuadraticCharacter(e) : FldNumElt -> GrpHeckeElt
            Example Char_dirichletQ (H43E1)
            Example Char_simple-char-ops (H43E2)
            DirichletCharacter(I, B) : RngOrdIdl, Tup -> GrpDrchNFElt, GrpDrchNF
            Example Char_dirichlet-hecke (H43E3)
            CentralCharacter(chi) : GrpDrchNFElt -> GrpDrchNFElt
            Example Char_central-chars (H43E4)
            DirichletCharacterOverNF(chi) : GrpDrchElt -> GrpDrchNFElt
            Example Char_dirich-chars-over-nf-and-q (H43E5)

      L-functions of Hecke Characters
            Example Char_lfunc-hecke (H43E6)

      Hecke Grössencharacters and their L-functions
            Grossencharacter(psi, chi, T) : GrpHeckeElt, GrpDrchNFElt, SeqEnum -> GrossenChar
            Grossencharacter(psi, T) : GrpHeckeElt, SeqEnum -> GrossenChar
            Conductor(GR) : GrossenChar -> RngOrdIdl, SeqEnum
            Components(GR) : GrossenChar -> Assoc
            Component(GR, P) : GrossenChar, RngOrdIdl -> GrpDrchNFEl
            Extend(GR, I) : GrossenChar, RngOrdIdl -> GrossenChar
            CentralCharacter(GR) : GrossenChar -> GrpDrchNFElt
            GrossenTwist(GR, D) : GrossenChar, List -> GrossenChar, GrpHecke
            TateTwist(GR, n) : GrossenChar, RngIntElt -> GrossenChar
            Example Char_grossenchar-gaussian (H43E7)
            Example Char_grossenchar-sqrt23 (H43E8)
            Example Char_grossenchar-symcubed-sqrt59 (H43E9)
            Example Char_grossen-char-cyclo5 (H43E10)
            Example Char_grossenchar-embedding (H43E11)
            Example Char_grossen-large-gamma (H43E12)
            Example Char_grossen-cyclo8 (H43E13)
            Example Char_hypgeom-mot (H43E14)

      Local Root Numbers
            RootNumber(GR, P) : GrossenChar, RngOrgIdl -> FldComElt
            RootNumber(GR, p) : GrossenChar, RngIntElt -> FldComElt
            RootNumbers(GR) : GrossenChar -> SeqEnum
            RootNumber(GR) : GrossenChar -> SeqEnum
            Example Char_rootno-27a (H43E15)
            Example Char_rohrlich-rootno (H43E16)

      Grössencharacters and Elliptic Curves
            Grossencharacter(E) : CrvEll -> GrossenChar
            EllipticCurve(GR) : GrossenChar -> CrvEll
            Example Char_grossenchar-and-ec (H43E17)

 
Bibliography

[Next][Prev] [Right] [____] [Up] [Index] [Root]