数学学科Seminar第2671讲 Andrews-Beck 分拆统计量和Appell-Lerch级数

创建时间:  2024/06/16  龚惠英   浏览次数:   返回

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:金沙威尼斯欢乐娱人城数学系

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.

上一条:金沙威尼斯欢乐娱人城核心数学研究所——几何与分析综合报告第85讲 体积型的闵可夫斯基不等式及其应用

下一条:数学学科Seminar第2670讲 截断的Theta函数恒等式的求和


数学学科Seminar第2671讲 Andrews-Beck 分拆统计量和Appell-Lerch级数

创建时间:  2024/06/16  龚惠英   浏览次数:   返回

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:金沙威尼斯欢乐娱人城数学系

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.

上一条:金沙威尼斯欢乐娱人城核心数学研究所——几何与分析综合报告第85讲 体积型的闵可夫斯基不等式及其应用

下一条:数学学科Seminar第2670讲 截断的Theta函数恒等式的求和