Construction of all polynomial relations among Dedekind eta functions of level N. (November 2019) - Hemmecke, Ralf; Radu, Silviu
Abstract: We describe an algorithm that, given a positive integer N, computes a Gröbner basis of the ideal of polynomial relations among Dedekind η -functions of level N, i.e., among the elements of { η ( δ 1 τ ), …, η ( δ n τ ) } where 1 = δ 1 < δ 2 < … < δ n = N are the positive divisors of N . More precisely, we find a finite generating set (which is also a Gröbner basis) of the ideal ker ⁡ ϕ where ϕ : Q [ E 1, …, E n ] → Q [ η ( δ 1 τ ), …, η ( δ n τ ) ], E k ↦ η ( δ k τ ), k = 1, …, n .