ModularEtaQuotientQSeriesInfinityTools(C, MODG)ΒΆ

qetamodeqqseriesinftool.spad line 79 [edit on github]

undocumented

coerce: EtaQuotientQSeriesInfinity C -> ModularFunctionQSeriesInfinity C if C has CommutativeRing

coerce(x) assumes that eqi is the representation of a modular eta-quotient with a cusp only at infinity and expands it into a Laurent series.

coerce: EtaQuotientQSeriesInfinity C -> QEtaLaurentSeries C

coerce(eqi) assumes that eqi is the representation of an eta-quotient and expands it into a Laurent series.

laurentExpansionInfinity: (QEtaSpecification, QEtaSpecification, PositiveInteger, NonNegativeInteger) -> QEtaLaurentSeries C

laurentExpansionInfinity(sspec,rspec,m,t) computes the $q$-series Laurent expansion corresponding to the disection of the eta-quotient given by rspec, with parameters (m,t) and multiplied by the etaquotient given by sspec. It corresponds to F_{s,r,m,t}(tau) as given through Equation eqref{eq:Ramanuja-Kolberg-Identity}.

laurentExpansionInfinity: QEtaSpecification -> QEtaLaurentSeries C

laurentExpansionInfinity(spec) computes the $q$-series Laurent expansion of the eta-quotient given by spec.

modularEtaQuotientInfinity: (QEtaSpecification, QEtaSpecification, PositiveInteger, NonNegativeInteger) -> ModularFunctionQSeriesInfinity C if C has CommutativeRing

modularEtaQuotientInfinity(sspec,rspec,m,t) returns the series expansion of the modular function given by the (m,t)-dissection of rspec and eta-quotient cofactor sspec at the cusp infinity. It checks whether the specification is indeed modular for the group respective by MODG.

modularEtaQuotientInfinity: (QEtaSpecification, QGeneratingFunctionVariable) -> ModularFunctionQSeriesInfinity C if C has CommutativeRing

modularEtaQuotientInfinity(sspec,dissect) returns modularEtaQuotientInfinity(sspec,rspec,m,t) where rspec=definingSpecification(dissect), m=multiplier(dissect), and t=offset(dissect).

modularEtaQuotientInfinity: QEtaSpecification -> ModularFunctionQSeriesInfinity C if C has CommutativeRing

modularEtaQuotientInfinity(rspec) checks whether rspec specifices modular eta-quotient wrt. the group that is represented by MODG and returns (expansion(etaQuotient(rspec)$EQI(C))$EQI(C))::A1(C).