q-rational series and analytic functions
报告题目：q-rational series and analytic functions
报告专家：刘治国 教授（华东师范大学）
报告时间：2023年6月19日16:00-17:00
报告地点：数学学院西303报告厅
报告摘要：
In 1973, Carlitz proved that if a function is analytic at origin, then it can be expanded into a q-rational series. Carlitz’s theorem is also called q-rational Maclaurin expansion. Almost thirty years later, Carlitz’s theorem was extended to the q-rational Taylor formula, which finds many important applications to q-series and number theory. With the help of q-rational series, we can overcome some extremely difficult problems in mathematics. q-rational series is a new and important mathematical research object that has not yet attracted widespread attention. In this talk, I will introduce some properties and applications of q-rational series.
专家简介：
刘治国，华东师范大学教授，博士生导师，主要研究领域为椭圆函数论、基本超几何级数理论和数论。刘治国教授不仅对天才数学家Ramanujan遗留的诸多问题有深入广泛的研究并取得了令人瞩目的研究成果，而且在国际上率先提出了q-偏微分方程的概念并将其应用到q-级数的研究中，开辟了该领域新的研究方向。 美国科学院院士George Andrews教授盛赞他“发展了令人称奇的数学方法”。 美国数学会会士Bruce Berndt教授及美国数学会会士Mourad E. H. Ismail教授曾公开撰文对刘治国教授的研究工作给予高度评价。刘治国教授已在 Adv. Math.、Trans. Amer. Math. Soc.、J. Combin. Theory Ser. A、 Pacific J. Math.、Bull. Lond. Math. Soc.、Ramanujan J.、J. Number Theory 等数学刊物上发表研究论文70多篇，相关论文被引用多达1400余次，曾荣获教育部高等学校自然科学研究成果奖二等奖等奖项。
邀请人：千国有