ModularEtaQuotientQSeriesTools(C, xiord, CX, xi, QMOD, trfs)ΒΆ
qetamodeqqseriestool.spad line 132 [edit on github]
- xiord: PositiveInteger 
- CX: Join(CommutativeRing, Algebra C) 
- xi: CX 
- QMOD: QEtaModularCategory 
ModularEtaQuotientQSeriesTools computes an eta quotient expansion of $g_{r,m,lambda}(gamma tau)$, $p_{r,m,t}(gammatau)$, $F_{s,r,m,t}(gammatau)$. See eqref{eq:g_r-m-lambda(gamma*tau)} and eqref{eq:F_s-r-m-t(gamma*tau)}.
- coerce: QEtaSpecificationRing C -> ModularFunctionQSeries(CX, trfs)
- coerce(x)effectively replaces each specification in the term of- xby the respective expansion at all the cusps.
- modularEtaQuotient: (QEtaSpecification, QEtaSpecification, PositiveInteger, NonNegativeInteger) -> ModularFunctionQSeries(CX, trfs)
- modularEtaQuotient(sspec, rspec, m, t)returns the series expansion of etaQuotient(- sspec,- rspec,- m,- t)$SymbolicModularEtaQuotientGamma(QMOD) at the respective cusps.
- modularEtaQuotient: QEtaSpecification -> ModularFunctionQSeries(CX, trfs)
- modularEtaQuotient(rspec)checks whether- rspecspecifices modular eta-quotient- wrt. QMOD and returns the Laurent expansion at the respective cusps. Due to Theorem 1 (Gordon, Hughes, Newman) in https://doi.- org/10.1515/crll.1996.472.1 we must only require that the weight of the modular eta-quotient is an integer and the other modular conditions are fulfilled, i.e. we only check that weakModular?(- rspec) is- trueinstead of modular?(- rspec).