Ramanujan’s two identities for Eisenstein Series
主 讲 人 ：刘治国 教授
活动时间：12月15日10时00分
地 点 ：欧乐影院 D203
讲座内容：
In his lost notebook, Srinivasa Ramanujan documented two important Eisenstein series identities intimately connected with fifth-degree modular equations. Historically, one of these identities played a pivotal role in Ramanujan’s derivation of his celebrated congruence for the partition function modulo 5: p(5n + 4) ≡ 0 (mod 5).
Over the past century, the investigation of Ramanujan’s identities has catalyzed significant progress in both modular forms theory and combinatorial analysis. In this presentation, I will introduce novel parametrizations of these two renowned identities through the framework of elliptic functions.
These parametrizations establish a systematic approach with applications in modular forms theory, proving especially valuable for deriving new identities that connect Eisenstein series with the Dedekind eta function. I will present several new results that illustrate the efficacy and broad applicability of this methodology.
主讲人介绍：
刘治国，华东师范大学欧乐影院
的二级教授及博士生导师，长期致力于数论与量子无穷级数理论的深入研究。主持多项国家自然科学基金项目，已在《Advances in Mathematics》《Transactions of AMS》《IMRN》等国际著名数学期刊上发表欧乐影院
论文80余篇。他成功提出了计算量子无穷级数和量子积分的新理论，被美国数学会会士Mourad E. H. Ismail教授赞誉为“Liu’s Calculus”。荣获包括1998年度王宽诚皇家学会研究奖学金以及2019年教育部高等学校自然科学研究成果奖二等奖等多项荣誉。