Overview
Built-in L-series RiemannZeta() : -> LSer Example Lseries_lseries-sig-riemann (H117E1) LSeries(K) : FldNum -> LSer Example Lseries_lseries-sig-dedekind (H117E2) Example Lseries_lseries-sig-dedekind2 (H117E3) Example Lseries_armitage (H117E4) LSeries(A) : ArtRep -> LSer Example Lseries_lseries-artin (H117E5) LSeries(E) : CrvEll -> LSer Example Lseries_lseries-sig-elliptic (H117E6) LSeries(E, K) : CrvEll, FldNum -> LSer Example Lseries_lseries-sig-ellnf (H117E7) LSeries(E, A) : CrvEll, ArtRep -> LSer Example Lseries_lseries-sig-ellartintwist (H117E8) LSeries(Chi) : GrpDrchElt -> LSer Example Lseries_lseries-sig-character (H117E9) LSeries(psi) : GrpHeckeElt -> LSer Example Lseries_lseries-sig-modfrm (H117E10)
Computing L-values Evaluate(L, s0) : LSer, FldComElt -> FldComElt CentralValue(L) : LSer -> FldComElt LStar(L, s0) : LSer, FldComElt -> FldComElt LTaylor(L,s0,n) : LSer, FldComElt, RngIntElt -> FldComElt Example Lseries_lseries-evaluate (H117E11)
Arithmetic with L-series L1 * L2 : LSer, LSer -> LSer L1 / L2 : LSer, LSer -> LSer TensorProduct(L1, L2, ExcFactors) : LSer, LSer, [<>] -> LSer
General L-series
Terminology
Constructing a General L-Series LSeries(weight, gamma, conductor, cffun) : FldReElt,[FldRatElt],FldReElt,Any -> LSer Example Lseries_checkfun (H117E12)
Setting the Coefficients LSetCoefficients(L,cffun) : LSer, Any ->
Specifying the Coefficients Later Example Lseries_lseries-lcfrequired (H117E13)
Generating the Coefficients from Local Factors
Accessing the Invariants LCfRequired(L) : LSer -> RngIntElt LGetCoefficients(L, N) : LSer, RngIntElt -> List EulerFactor(L, p) : LSer, RngIntElt -> .var Degree : RngIntElt : var Precision: RngIntElt Default: desGiven an L-series and a prime p, this computes thepth Euler factor, either as a polynomial or a power series.The optional parameter Degree will truncate the series to that length,and the optional parameter Precision is of use when the series isdefined over the complex numbers. Sign(L) : LSer -> . GammaFactors(L) : LSer -> Seqenum LSeriesData(L) : LSer -> Info Example Lseries_lseries-invariants (H117E14) Factorization(L) : LSer -> SeqEnum[Tup] Example Lseries_lseries-invariants (H117E15)
Precision LSetPrecision(L,precision) : LSer, RngIntElt ->
L-series with Unusual Coefficient Growth
Computing L(s) when Im(s) is Large (ImS Parameter)
Implementation of L-series Computations (Asymptotics Parameter)
Verbose Printing
Advanced Examples
Self-made L-series of an Elliptic Curve Example Lseries_lseries-elliptic-selfmade (H117E16)
Self-made Dedekind Zeta Function Example Lseries_lseries-dedekind-selfmade (H117E17)
L-series of a Genus 2 Hyperelliptic Curve Example Lseries_lseries-genus2 (H117E18)
Experimental Mathematics for Small Conductor Example Lseries_lseries-experimental (H117E19)
Tensor Product of L-series Coming from l-adic Representations Example Lseries_lseries-tensor (H117E20)
Non-abelian Twist of an Elliptic Curve Example Lseries_lseries-nonabtwist (H117E21)
Other Tensor Products Example Lseries_marks-tensorprod (H117E22) Example Lseries_level1-modform (H117E23) Example Lseries_siegel-modular-form (H117E24) Example Lseries_tensprod-overK (H117E25)
Symmetric Powers SymmetricPower(L, m) : LSer, RngIntElt -> LSer Example Lseries_sympow (H117E26)
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