Radial limits of mock theta functions
Radial limits of mock theta functions
复制标题
模拟 theta 函数的径向极限
DOI：
10.1186/s40687-015-0035-8
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发表时间：
2014
影响因子：
1.2
通讯作者：
Larry Rolen
中科院分区：
文献类型：
--
作者：
K. Bringmann;Larry Rolen
受Ramanujan对模拟函数的原始定义的启发，许多作者已经考虑了明确确定它们在尖端处的行为的问题。此外，这些例子已经被连接到重要的对象，如量子模形式和秩和曲柄由Folsom， Ono和Rhoades。在这里，我们解决了对于任意权重$$\frac{1}{2}$$ 12 mock theta函数显式理解Ramanujan定义的一般问题，回答了Rhoades的问题。此外，作为副产物，我们的结果给出了一个大的、显式的模形式族。
Inspired by the original definition of mock theta functions by Ramanujan, a number of authors have considered the question of explicitly determining their behavior at the cusps. Moreover, these examples have been connected to important objects such as quantum modular forms and ranks and cranks by Folsom, Ono, and Rhoades. Here, we solve the general problem of understanding Ramanujan’s definition explicitly for any weight $$\frac{1}{2}$$12 mock theta function, answering a question of Rhoades. Moreover, as a side product, our results give a large, explicit family of modular forms.