江苏大学夏先伟教授学术报告

发布时间:2021年05月10日 作者:贺兵   阅读次数:[]

报告题目:New truncated theorems for three classic theta function identities

报告人:夏先伟教授

报告时间:2021/05/21   10:00-11:30

报告地点:腾讯会议  467 362 170

报告摘要In 2012, Andrews and Merca derived a truncated version of Euler's pentagonal

number theory.  Their work inspired several mathematicians to work on truncated theta series including Guo and Zeng, who examined two other classical theta series identities of Gauss. In this paper, revisiting these three theta series identities of Euler and Gauss, we obtain new truncated theorems.  As corollaries of our results, we obtain infinite families of linear inequalities involving the  partition function, the overpartition function and the pod partition function. These inequalities imply the positive result of Andrews and Merca on the  partition function as well as a conjecture on the overpartition function, which was given by Guo and Zeng and proved independently by Mao and Yee. We will also provide a unified combinatorial treatment for our results.

报告人简介:夏先伟,教授,博士生导师,江苏省杰青获得者。2010年博士毕业于南开大学,师从陈永川院士,主要研究整数分拆、特殊函数。在Math. Comput., Proc. Edinb. Math. Soc., Pacific J. Math.JNT, Acta Arithm.等期刊上发表了60多篇论文,主持国家自然科学基金项目多项。




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