@

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}