Construction of all polynomial relations among Dedekind eta functions of level N. (November 2019)

• Record Type: Journal Article
• Authors: Hemmecke, Ralf; Radu, Silviu
• Is Part Of: Journal of symbolic computation. Volume 95(2019)
• Page Start: 39
• Page End: 52
• Publication Date: 2019-11
• Subjects: Dedekind η function -- Modular functions -- Modular equations -- Ideal of relations -- Gröbner basis; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2018.10.001
• Languages: English
• ISSNs: 0747-7171

Abstract

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 .