报告题目：New truncated sums the Jacobi triple product identity and the quintuple product identity

报告人：夏先伟

负责人：李雪珊

报告时间：2025年10月16日15：00-16:00

报告地点：腾讯会议，会议号：416 322 863

参加人员：教师，研究生

报告摘要：In their study of the truncated sums of the classical theta functions, Andrews-Merca and Guo-Zeng posed a conjecture on truncated sums of a special case of the Jacobi triple product identity which was confirmed independently by Mao and Yee. In 2016, Chan, Ho and Mao examined the truncated series arising from two consequences of the quintuple product identity. In this talk, we establish an explicit series form with nonnegative coefficients on a new truncated sum of a special cases of the Jacobi triple product identity by taking different truncated series which is stronger than the conjecture due to Andrews-Merca and Guo-Zeng. As a corollary of our results, we obtain a new truncated sums of Jacobi's identity which implies another conjecture given by Guo and Zeng. In addition, we determine the signs of coefficients of new truncated sums of two well-known identities derived from the quintuple product identity which can be considered as the companion results of a theorem proved by Chan, Ho and Mao.

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组合数学中心,主要研究整数分拆、特殊函数。在Math. Comput.,JCTA, Europ. J. Combin, Adv. Appl. Math，JNT, Acta Arithm.等国际主流期刊上发表了多篇学术论文。主持多项国家自然科学基金项目。