Dancing samba with Ramanujan partition congruences

The article presents an algorithm to compute a C[t]-module basis G for a given subalgebra A over a polynomial ring R=C[x] with a Euclidean domain C as the domain of coefficients and t a given element of A. The reduction modulo G allows a subalgebra membership test. The algorithm also works for more...

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Veröffentlicht in:	Journal of symbolic computation Jg. 84; S. 14 - 24
1. Verfasser:	Hemmecke, Ralf
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Elsevier Ltd 01.01.2018
Schlagworte:	Number theoretic algorithm Partition identities Subalgebra basis Number theoretic algorithm Partition identities Subalgebra basis
ISSN:	0747-7171, 1095-855X
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	The article presents an algorithm to compute a C[t]-module basis G for a given subalgebra A over a polynomial ring R=C[x] with a Euclidean domain C as the domain of coefficients and t a given element of A. The reduction modulo G allows a subalgebra membership test. The algorithm also works for more general rings R, in particular for a ring R⊂C((q)) with the property that f∈R is zero if and only if the order of f is positive. As an application, we algorithmically derive an explicit identity (in terms of quotients of Dedekind η-functions and Klein's j-invariant) that shows that p(11n+6) is divisible by 11 for every natural number n where p(n) denotes the number of partitions of n.
ISSN:	0747-7171 1095-855X
DOI:	10.1016/j.jsc.2017.02.001