Dancing samba with Ramanujan partition congruences. (January 2018) - Hemmecke, Ralf
Abstract: 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 ( 11 n + 6 ) is divisible by 11 for every natural number n where p ( n ) denotes the number of partitions of n .