The Generators of all Polynomial Relations Among Jacobi Theta Functions

  • Ralf HemmeckeEmail author
  • Cristian-Silviu Radu
  • Liangjie Ye
Part of the Texts & Monographs in Symbolic Computation book series (TEXTSMONOGR)


In this article, we consider the classical Jacobi theta functions \(\theta _i(z)\), \(i=1,2,3,4\) and show that the ideal of all polynomial relations among them with coefficients in \(K :=\mathbb {Q}(\theta _2(0|\tau ),\theta _3(0|\tau ),\theta _4(0|\tau ))\) is generated by just two polynomials, that correspond to well known identities among Jacobi theta functions.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Ralf Hemmecke
    • 1
    Email author
  • Cristian-Silviu Radu
    • 1
  • Liangjie Ye
    • 1
  1. 1.Research Institute for Symbolic ComputationJohannes Kepler UniversityLinzAustria

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