Theta vocabulary I

S. Kharchev, A. Zabrodin

Research output: Contribution to journalReview articlepeer-review

18 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)19-31
Number of pages13
JournalJournal of Geometry and Physics
Publication statusPublished - 1 Aug 2015
Externally publishedYes


  • Addition formulae
  • Elliptic functions
  • Identities for theta functions


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