QEtaRamanujanKolberg(C, QMOD)ΒΆ

qetark.spad line 755 [edit on github]

QEtaRamanujanKolberg provides functions to compute Ramanujan-Kolberg identities by an algorithm that was developed by Radu in cite{Radu_RamanujanKolberg_2015} (`DOI=10.1016/j.jsc.2014.09.018 <https://doi.org/10.1016/j.jsc.2014.09.018>`_), see RISC Report 16-06 <https://www.risc.jku.``at/publications/download/risc_5069/zzz3`.pdf>`_. See also at the top of the qetark.spad file where this package is implemented. This package builds on the work of cite{ChenDuZhao_FindingModularFunctionsRamanujan_2019} and finds identities with generalized eta-quotients.

findIdentity: (PositiveInteger, List List Integer, QEtaSpecification, PositiveInteger, NonNegativeInteger, List List Integer) -> QEtaRamanujanKolbergIdentity C

findIdentity(nn, sidxs, rspec, m, k, bidxs) returns all data for a Ramanujan-Kolberg identity where the indices for the cofactor and the generalized eta-quotients on the right-hand side are given by sidxs and bidxs, respectively.

findIdentity: (PositiveInteger, List List Integer, QEtaSpecification, PositiveInteger, NonNegativeInteger, List QEtaSpecification) -> QEtaRamanujanKolbergIdentity C

findIdentity(nn, idxs, rspec, m, k, mgens) returns all data for a Ramanujan-Kolberg identity where the cofactor may only involve generalized eta-functions given through the indices idxs. Note that elements from mspecs that specify constant generalized eta-quotients will be removed.

findIdentity: (PositiveInteger, List List Integer, QEtaSpecification, PositiveInteger, NonNegativeInteger, QEtaRamanujanKolbergIdentity C) -> QEtaRamanujanKolbergIdentity C

findIdentity(nn, sidxs, rspec, m, k, id) returns all data for a Ramanujan-Kolberg identity. The basis elements are taken from a previously computed identity, if possible.

findIdentity: (PositiveInteger, QEtaSpecification, PositiveInteger, NonNegativeInteger, List List Integer) -> QEtaRamanujanKolbergIdentity C

findIdentity(nn,rspec,m,k,idxs) returns findIdentity(nn,idxs,rspec,m,k,idxs)

findIdentity: (QEtaSpecification, QEtaSpecification, PositiveInteger, NonNegativeInteger, List List Integer) -> QEtaRamanujanKolbergIdentity C

findIdentity(sspec, rspec, m, k, idxs) returns all data for a Ramanujan-Kolberg identity where the right-hand side may only involve generalized eta-quotients that are given through the indices idxs.

findIdentity: (QEtaSpecification, QEtaSpecification, PositiveInteger, NonNegativeInteger, List QEtaSpecification) -> QEtaRamanujanKolbergIdentity C

findIdentity(sspec, rspec, m, k, mspecs) returns all data for a Ramanujan-Kolberg identity. Note that elements from mspecs that specify constant generalized eta-quotients will be removed.

findIdentity: (QEtaSpecification, QEtaSpecification, PositiveInteger, NonNegativeInteger, List QEtaSpecification, QEtaAlgebraBasis QEtaExtendedAlgebra(C, ModularFunctionQSeriesInfinity C, QEtaLazyAlgebra(C, Polynomial C))) -> QEtaRamanujanKolbergIdentity C

findIdentity(sspec, rspec, m, k, mspecs, xab) returns all data for a Ramanujan-Kolberg identity. It is assumed that mspecs describe the Mi variables in xab in the same order.

findIdentity: (QEtaSpecification, QEtaSpecification, PositiveInteger, NonNegativeInteger, QEtaRamanujanKolbergIdentity C) -> QEtaRamanujanKolbergIdentity C

findIdentity(sspec, rspec, m, k, id) returns all data for a Ramanujan-Kolberg identity. The basis elements are taken from a previously computed identity, if possible.