报告时间：2026年3月14日（周六）上午 10:30-11:30
报告地点：苏州大学数学楼一楼报告厅
报告人：刘治国 教授，华东师范大学
报告摘要：
In the theory of elliptic functions, the partial fraction decomposition of functions with simple poles serves as a powerful bridge between local singularity analysis and global Fourier series expansions. This talk presents a systematic approach to deriving classical and new identities for elliptic functions using a specific decomposition theorem centered on the logarithmic derivative of the Jacobi theta function $\theta_1(z|\tau)$.
The utility of this method is showcased through the derivation of several elegant identities recently discussed in the literature. Specifically, we provide a rigorous proof for two significant identities involving the Dedekind eta function $\eta(\tau)$ and the Legendre symbol. Finally, by taking the limit as $z \to 0$ and specializing $z = \pi/3$, we recover several of Ramanujan's famous Eisenstein series identities and $q$-series products. This approach not only provides a unified framework for these identities but also highlights the deep arithmetic properties embedded within the quasi-periodicity of theta functions.
报告人简介：
刘治国，华东师范大学数学系教授，博士生导师。在椭圆函数论、q-级数理论、解析数论等领域取得了许多原创性的研究成果。其中之一是他提出了计算量子无穷级数和量子积分的新理论，该理论被美国数学会会士Mourad E. H. Ismail教授在公开发表的论文中称为“Liu's Calculus”。曾被英国皇家学会破格授予“王宽诚皇家学会研究奖学金”。目前已在《Adv. Math.》、《J. Combin. Theory Ser. A》、《Pacific J. Math.》、《Bull. London Math. Soc.》、《Ramanujan J.》、《J. Number Theory》等国际重要数学刊物上发表70多篇研究论文，并主持了多项国家自然科学基金项目。
邀请人：马欣荣 毛仁荣