Elliptic function based algorithms to prove Jacobi theta function relations. (November 2018)

• Record Type: Journal Article
• Authors: Ye, Liangjie
• Is Part Of: Journal of symbolic computation. Volume 89(2018)
• Page Start: 171
• Page End: 193
• Publication Date: 2018-11
• Subjects: Jacobi theta functions -- Modular forms -- Algorithmic zero-recognition -- Computer algebra -- Automatic proving of special function identities; 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.2017.11.011
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: In this paper we prove identities involving the classical Jacobi theta functions of the form ∑ c ( i 1, i 2, i 3, i 4 ) θ 1 ( z | τ ) i 1 θ 2 ( z | τ ) i 2 θ 3 ( z | τ ) i 3 θ 4 ( z | τ ) i 4 = 0 with c ( i 1, i 2, i 3, i 4 ) ∈ K [ Θ ], where K is a computable field and Θ : = { θ 1 ( 2 k + 1 ) ( 0 | τ ) : k ∈ N } ∪ { θ j ( 2 k ) ( 0 | τ ) : k ∈ N and j = 2, 3, 4 } . We give two algorithms that solve this problem. The second algorithm is simpler and works in a restricted input class.