2015/02/28 by S. Kharchev, A. Zabrodin
Mathematics · #math.CA #math.CV
paper · pdf · doi:10.1016/j.geomphys.2015.03.010
19 pages, minor corrections
arxiv created 2015/04/07 · arxiv updated 2015/05/20
This paper is an annotated list of transformation properties and identities satisfied by the four theta functions θ1, θ2, θ3, θ4 of one complex variable, presented in a ready-to-use form. An attempt is made to reveal a pattern behind various identities for the theta-functions. It is shown that all possible 3, 4 and 5-term identities of degree four emerge as algebraic consequences of the six fundamental bilinear 3-term identities connecting the theta-functions with modular parameters τ and 2τ.