T-系数法在Q-级数理论中的应用
报告专家：马欣荣 教授（苏州大学）
报告时间：2026年4月2日（星期四）10：30-11：30
报告地点：数学学院西303
报告摘要：
My report is about a uniform approach—the t-coefficient method—to basic hypergeometric series, which was proposed originally by myself in 2012. The report is divided into three parts.
In the first part is some new and elementary proofs via the t-coefficient method for many partial theta function identities due to Alladi, Andrews, and Warnaar,as well as some classical summation formulas such as Ramanujan’s ${}_1\psi_1$ summation formula are obtained.
In the second part,by the t-coefficient method,we establish a general series expansion formula with five free parameters for the product of arbitrary two Jacobi theta functions. It embodies the triple, quintuple, sextuple and septuple theta function product identities and the generalized Schröter formula.
In the third part, I will report a general series expansion formula for the product of arbitrary two theta functions with bases, and how the products of arbitrary finitely many theta functions and theta identities associated with Ramanujan’s circular summation is derived.
专家简介：
马欣荣, 苏州大学教授、博士生导师。先后师从我国著名数学家徐利治教授和朱烈教授。1995 年博士毕业于大连理工大学应用数学研究所, 1996 年在苏州大学博士后流动站从事组合数学研究。目前已主持完成国家自然科学基金面上项目多项。在组合反演、$q$-级数理论等方面发表了60多篇论文, 取得了多项原创性成果, 其中最具代表性的成果是 $(f,g)$-反演公式和 $(f,g)$-展开公式。
邀请人：千国有
