报告题目：Identities, Inequalities and Congruences for Odd Ranks and k-marked Odd Durfee Symbols

报告人：夏先伟 教授（苏州科技大学）

报告时间：2021 年 11 月 11 日（星期四） 15:30-16:30

报告地点：腾讯会议       ID：274 298 122

校内联系人：陈曦         84708351-8025

报告摘要: In 2007, Andrews introduced the odd rank of  odd Durfee symbols. Let  denote the number of odd Durfee symbols of n with odd rank m,  and  be the number of odd Durfee symbols of n with odd rank congruent to r modulo m. In this paper, we give the generating functions for  by utilizing some identities involving Appell-Lerch sums  and a universal mock theta function . Based on these  formulas, we  determine the signs of  for all  and  . In particular, we prove that . Moreover, let  denote the number of k-marked odd Durfee symbols of n. Andrews conjectured that and   are even with  and  which were confirmed by Wang. In this paper, we found new congruences for . In particular,  for k=2 or 3, we give characterizations of n such that  is odd and  prove that   take even values with probability 1 for .

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，师从陈永川教授，主要研究组合数学、特殊函数与整数分拆，在包括Math. Comput., Proc. Edinb. Math. Soc., Adv. Appl. Math., Pacific J. Math., European J. Combin., Acta Arith., J. Number Theory 等期刊上发表了多篇。主持两项国家自然科学基金面上项目。