Department of Mathematics and Computer Science, Emory University, Atlanta, GA 30322, USA.
Proc Natl Acad Sci U S A. 2013 Apr 9;110(15):5765-8. doi: 10.1073/pnas.1300345110. Epub 2013 Mar 27.
In his famous deathbed letter, Ramanujan introduced the notion of a mock theta function, and he offered some alleged examples. Recent work by Zwegers [Zwegers S (2001) Contemp Math 291:268-277 and Zwegers S (2002) PhD thesis (Univ of Utrecht, Utrecht, The Netherlands)] has elucidated the theory encompassing these examples. They are holomorphic parts of special harmonic weak Maass forms. Despite this understanding, little attention has been given to Ramanujan's original definition. Here, we prove that Ramanujan's examples do indeed satisfy his original definition.
在他著名的临终信中，拉马努金引入了拟theta 函数的概念，并给出了一些据称的例子。 Zwegers 的近期工作[Zwegers S (2001) Contemp Math 291:268-277 and Zwegers S (2002) PhD thesis (Univ of Utrecht, Utrecht, The Netherlands)]阐明了包含这些例子的理论。它们是特殊调和弱马瑟斯形式的全纯部分。尽管有了这种理解，但对拉马努金的原始定义关注甚少。在这里，我们证明了拉马努金的例子确实满足他的原始定义。
