QModularGamma0ΒΆ
qetamod.spad line 245 [edit on github]
QModularGamma0 provides functions to check modularity for Gamma0. TODO: conditionCoEtaQuotient?(nn,rspec,m,t) returns true iff all the conditions for the parameters are fulfilled. This checks whether (nn,rspec,m,t) is in Delta^* as defined in Definition~ref{def:condition-co-eta-quotient-gamma0} in qeta.tex and in Definition 35 of cite{Radu_RamanujanKolberg_2015} 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,rspec,m,t) is an element of Delta^* as defined in Definition~ref{def:condition-co-eta-quotient-gamma0}. minimalLevelCoEtaQuotient(rspec,m,t) returns the smallest nn of candidateLevalsCoEtaQuotient(rspec,m,t). Note that one might have to use a bigger nn, because the level might still be too small to find a cofactor an example is for rspec=[[1,-1],[7,1]], m=9, t=5 where this function returns 21, but one would have to use 42.
- 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