论文标题
模拟theta功能和相关组合学
Mock theta functions and related combinatorics
论文作者
论文摘要
在本文中，我们添加了有关模拟Theta功能的组合性质的文献，Ramanujan在1920年给Hardy的最后一封信中介绍了一个好奇的$ Q $ hyphepericers系列，我们现在知道这是模拟模块化形式的重要例子。我们的工作灵感来自贝克的猜想，现在是安德鲁斯的定理，与欧拉的身份相关：与$ n $分区的所有分区中的零件中的零件数量超过了$ n $的零件数量，分为$ n $的零件数量等于分区的数量，等于只有一个分区的数量，甚至只有一个（可能重复出现）零件，甚至所有其他零件）。我们建立了与第三阶模拟theta函数$ω（q），ν（q）$和$ ϕ（q）$相关的贝克型身份。我们的证明本质上是分析性和组合性的，并且涉及模拟theta产生功能和组合射击。
In this paper we add to the literature on the combinatorial nature of the mock theta functions, a collection of curious $q$-hypergeometric series introduced by Ramanujan in his last letter to Hardy in 1920, which we now know to be important examples of mock modular forms. Our work is inspired by Beck's conjecture, now a theorem of Andrews, related to Euler's identity: the excess of the number of parts in all partitions of $n$ into odd parts over the number of partitions of $n$ into distinct parts is equal to the number of partitions with only one (possibly repeated) even part and all other parts odd. We establish Beck-type identities associated to partition identities due to Andrews, Dixit, and Yee for the third order mock theta functions $ω(q), ν(q)$, and $ϕ(q)$. Our proofs are both analytic and combinatorial in nature, and involve mock theta generating functions and combinatorial bijections.
