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 ofx
by 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 whetherrspec
specifices modular eta-quotientwrt
. 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
) istrue
instead of modular?(rspec
).