Ralf Hemmecke, Silviu Radu, Liangjie Ye,
"The Generators of all Polynomial Relations among Jacobi Theta Functions"
, in Johannes Blümlein and Carsten Schneider and Peter Paule: Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory, Serie Texts & Monographs in Symbolic Computation, Nummer 18-09, Springer International Publishing, Cham, Seite(n) 259-268, 2019, ISBN: 978-3-030-04479-4
Original Titel:
The Generators of all Polynomial Relations among Jacobi Theta Functions
Sprache des Titels:
Englisch
Original Buchtitel:
Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory
Original Kurzfassung:
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. Also available as RISC Report 18-09 http://www.risc.jku.at/publications/download/risc_5719/thetarelations.pdf