报告题目 (Title)：Truncated sums of theta function identities（截断的Theta函数恒等式的求和）
报告人 (Speaker)：夏先伟教授（苏州科技大学）
报告时间 (Time)：2024年06月16日(周日) 13：00-15：00
报告地点 (Place)：校本部GJ303
邀请人(Inviter)：陈旦旦
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 Jacibi'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.