AN ANALOGUE OF AN IDENTITY OF JACOBI
Abstract H. H. Chan, K. S. Chua and P. Solé [‘Quadratic iterations to $\pi $ associated to elliptic functions to the cubic and septic base’, Trans. Amer. Math. Soc. 355 (4) (2002), 1505–1520] found that, for each positive integer d , there are theta series $A_d, B_d$ and $C_d$ of weight one that satisfy the Pythagoras-like relationship $A_d^2=B_d^2+C_d^2$ . In this article, we show that there are two collections of theta series $A_{b,d}, B_{b,d}$ and $C_{b,d}$ of weight one that satisfy $A_{b,d}^2=B_{b,d}^2+C_{b,d}^2,$ where b and d are certain integers.
Authors
- Heng Huat Chan (ORCID: https://orcid.org/0000-0002-9215-0895)
- Patrick Solé (ORCID: https://orcid.org/0000-0002-4078-8301)
- Song Heng Chan (ORCID: https://orcid.org/0000-0002-3696-2768)
Institutions
- Centre National de la Recherche Scientifique (FR)
- Shandong University (CN)
- Nanyang Technological University (SG)
- Aix-Marseille Université (FR)
- Institut Polytechnique de Bordeaux (FR)
Publication Details
- Journal
- Bulletin of the Australian Mathematical Society
- Published
- 2025-02-07
- DOI
- https://doi.org/10.1017/s0004972724001412
- Primary Topic
- Advanced Mathematical Identities
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Ministry of Education - Singapore