RISC JKU
  • @incollection{RISC5913,
    author = {Ralf Hemmecke and Silviu Radu and Liangjie Ye},
    title = {{The Generators of all Polynomial Relations among Jacobi Theta Functions}},
    booktitle = {{Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory}},
    language = {english},
    abstract = {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 $K :=\setQ(\theta_2(0|\tau),\theta_3(0|\tau),\theta_4(0|\tau))$ is generated by just two polynomials, that correspond to well known identities among Jacobi theta functions. },
    series = {Texts & Monographs in Symbolic Computation},
    number = {18-09},
    pages = {259--268},
    publisher = {Springer International Publishing},
    address = {Cham},
    isbn_issn = {978-3-030-04479-4},
    year = {2019},
    note = {Also available as RISC Report 18-09 http://www.risc.jku.at/publications/download/risc_5719/thetarelations.pdf},
    editor = {Johannes Blümlein and Carsten Schneider and Peter Paule},
    refereed = {yes},
    length = {9},
    url = {https://doi.org/10.1007/978-3-030-04480-0_11}
    }