QModularGamma1ΒΆ
qetamod.spad line 342 [edit on github]
QModularGamma1 provides functions to check modularity for Gamma1. TODO: conditionCoEtaQuotient?(nn,rspec,m,t) returns true iff the conditions in Chapter 10 of cite{ChenDuZhao_FindingModularFunctionsRamanujan_2019} just before Theorem 10.1 are fulfilled. See Definition~ref{def:condition-co-eta-quotient-gamma1}. These are conditions for the existence of a product of eta- and generalized eta-quotient to exist as a cofactor for a disection of such a quotient. The parameter rbar specifies the generalized eta-quotient via etaQuotient(rbar). These are slight modifications of conditions appearing in Definition 35 of cite{Radu_RamanujanKolberg_2015} in case the defining eta-quotient is not a generalized one. candidateLevelsCoEtaQuotient(rspec,m,t) returns an ascendingly sorted list of the nn up to 24*m*level(rspec) such that conditionCoEtaQuotient?(nn,rspec,m,t) is true, i.e. that (nn,mm,rbar m,t) fulfills the 10 conditions as defined in Section 10 of cite{ChenDuZhao_FindingModularFunctionsRamanujan_2019}. The parameter rbar specifies the generalized eta-quotient via etaQuotient(rbar).
- candidateLevelsCoEtaQuotient: (QEtaSpecification, PositiveInteger, NonNegativeInteger) -> List PositiveInteger
- conditionCoEtaQuotient?: (PositiveInteger, QEtaSpecification, PositiveInteger, NonNegativeInteger) -> Boolean
- minimalLevelCoEtaQuotient: (QEtaSpecification, PositiveInteger, NonNegativeInteger) -> PositiveInteger
- minimalLevelCoEtaQuotient: (QPochhammerSpecification, PositiveInteger, NonNegativeInteger) -> PositiveInteger
- minimalLevelCoEtaQuotient: QGeneratingFunctionVariable -> PositiveInteger