Overview
Built-in L-series RiemannZeta() : -> LSer Example Lseries_lseries-sig-riemann (H108E1) LSeries(K) : FldNum -> LSer Example Lseries_lseries-sig-dedekind (H108E2) LSeries(E) : CrvEll -> LSer Example Lseries_lseries-sig-elliptic (H108E3) LSeries(E,K) : CrvEll, FldNum -> LSer Example Lseries_lseries-sig-ellnf (H108E4) LSeries(Chi) : GrpDrchElt -> LSer Example Lseries_lseries-sig-character (H108E5) LSeries(f) : ModFrmElt -> LSer Example Lseries_lseries-sig-modfrm (H108E6)
Computing L-values Evaluate(L,s0) : LSer, FldComElt -> FldComElt LStar(L,s0) : LSer, FldComElt -> FldComElt LTaylor(L,s0,n) : LSer, FldComElt, RngIntElt -> FldComElt Example Lseries_lseries-evaluate (H108E7)
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 (H108E8)
Setting the Coefficients LSetCoefficients(L,cffun) : LSer, Any ->
Specifying the Coefficients Later Example Lseries_lseries-lcfrequired (H108E9)
Generating the Coefficients from Local Factors
Accessing the Invariants LCfRequired(L) : LSer -> RngIntElt LGetCoefficients(L,N) : LSer, RngIntElt -> List LSeriesData(L) : LSer -> Info Example Lseries_lseries-invariants (H108E10)
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 (H108E11)
Self-made Dedekind Zeta Function Example Lseries_lseries-dedekind-selfmade (H108E12)
L-series of a Genus 2 Hyperelliptic Curve Example Lseries_lseries-genus2 (H108E13)
Experimental Mathematics for Small Conductor Example Lseries_lseries-experimental (H108E14)
Tensor Product of L-series Coming from l-adic Representations Example Lseries_lseries-tensor (H108E15)
Non-abelian Twist of an Elliptic Curve
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