The Generators of all Polynomial Relations among Jacobi Theta Functions

Ralf Hemmecke; Silviu Radu; Liangjie Ye

doi:10.1007/978-3-030-04480-0_11

The Generators of all Polynomial Relations among Jacobi Theta Functions

Ralf Hemmecke
, Silviu Radu
, Liangjie Ye

Institut für Symbolisches Rechnen

Publikation: Beitrag in Buch/Bericht/Konferenzband › Kapitel › Begutachtung

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. Also available as RISC Report 18-09 http://www.risc.jku.at/publications/download/risc_5719/thetarelations.pdf

Originalsprache	Englisch
Titel	Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory
Herausgeber*innen	Johannes Blümlein and Carsten Schneider and Peter Paule
Erscheinungsort	Cham
Verlag	Springer International Publishing
Seiten	259-268
Seitenumfang	9
ISBN (Print)	978-3-030-04479-4
DOIs	https://doi.org/10.1007/978-3-030-04480-0_11
Publikationsstatus	Veröffentlicht - 2019

Publikationsreihe

Name	Texts & Monographs in Symbolic Computation

Wissenschaftszweige

101 Mathematik
101001 Algebra
101005 Computeralgebra
101009 Geometrie
101012 Kombinatorik
101013 Mathematische Logik
101020 Technische Mathematik

JKU-Schwerpunkte

Digital Transformation

Zugriff auf Dokument

10.1007/978-3-030-04480-0_11

Dieses zitieren

Hemmecke, R., Radu, S., & Ye, L. (2019). The Generators of all Polynomial Relations among Jacobi Theta Functions. in Johannes Blümlein and Carsten Schneider and Peter Paule (Hrsg.), Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory (S. 259-268). (Texts & Monographs in Symbolic Computation). Springer International Publishing. https://doi.org/10.1007/978-3-030-04480-0_11

Hemmecke, Ralf ; Radu, Silviu ; Ye, Liangjie. / The Generators of all Polynomial Relations among Jacobi Theta Functions. Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory. Hrsg. / Johannes Blümlein and Carsten Schneider and Peter Paule. Cham : Springer International Publishing, 2019. S. 259-268 (Texts & Monographs in Symbolic Computation).

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abstract = "In this article, we consider the classical Jacobi theta functions \$\textbackslash{}theta\_i(z)\$, \$i=1,2,3,4\$ and show that the ideal of all polynomial relations among them with coefficients in \$K :=\textbackslash{}setQ(\textbackslash{}theta\_2(0|\textbackslash{}tau),\textbackslash{}theta\_3(0|\textbackslash{}tau),\textbackslash{}theta\_4(0|\textbackslash{}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",

author = "Ralf Hemmecke and Silviu Radu and Liangjie Ye",

year = "2019",

doi = "10.1007/978-3-030-04480-0\_11",

language = "English",

isbn = "978-3-030-04479-4",

series = "Texts \& Monographs in Symbolic Computation",

publisher = "Springer International Publishing",

pages = "259--268",

editor = "\{Johannes Bl{\"u}mlein and Carsten Schneider and Peter Paule\}",

booktitle = "Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory",

}

Hemmecke, R , Radu, S & Ye, L 2019, The Generators of all Polynomial Relations among Jacobi Theta Functions. in Johannes Blümlein and Carsten Schneider and Peter Paule (Hrsg.), Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory. Texts & Monographs in Symbolic Computation, Springer International Publishing, Cham, S. 259-268. https://doi.org/10.1007/978-3-030-04480-0_11

The Generators of all Polynomial Relations among Jacobi Theta Functions. / Hemmecke, Ralf ; Radu, Silviu; Ye, Liangjie.
Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory. Hrsg. / Johannes Blümlein and Carsten Schneider and Peter Paule. Cham: Springer International Publishing, 2019. S. 259-268 (Texts & Monographs in Symbolic Computation).

Publikation: Beitrag in Buch/Bericht/Konferenzband › Kapitel › Begutachtung

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AB - 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

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Hemmecke R , Radu S, Ye L. The Generators of all Polynomial Relations among Jacobi Theta Functions. in Johannes Blümlein and Carsten Schneider and Peter Paule, Hrsg., Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory. Cham: Springer International Publishing. 2019. S. 259-268. (Texts & Monographs in Symbolic Computation). doi: 10.1007/978-3-030-04480-0_11