报告题目 (Title)：Andrews-Beck partition statistics and Appell-Lerch series（Andrews-Beck 分拆统计量和Appell-Lerch级数）
报告人 (Speaker)：朱晓杰博士（华东师范大学）
报告时间 (Time)：2024年06月16日(周日) 15:00-16:00
报告地点 (Place)：校本部GJ303
邀请人(Inviter)：陈旦旦
主办部门：永利数学系
报告摘要： In 2021, two partitions statistics, NT(r; m; n) and M_w(r; m; n), were proposed by Andrews and he proved some congruences conjectured by Beck. Since then, variations of Andrews-Beck type congruences were studied by many authors. Recently, Mao established the modular approach for analyzing the difference NT(s,k,n)-NT(k-s,k,n) and proved many identities by applying the theory of mock modular forms. In the current work (joint with Rong Chen), we study the p-dissections of NT(s,k,n)-NT(k-s,k,n) and show that they are sums of Appell-Lerch series and modular functions on Gamma_1(p). Our method relies heavily on the theory of (generalized) Appell-Lerch series. In this talk, we will focus on the modularity of the functions used in our work. In particular, we show how the theory of nonholomorphic Jacobi forms, U_pk operators, generalized eta-products are used in our work.
