Eta-quotients and theta functions
Eta-quotients and theta functions
复制标题
eta 商和 theta 函数
DOI：
10.1016/j.aim.2013.03.019
复制
发表时间：
2013
影响因子：
1.7
通讯作者：
R. Oliver
中科院分区：
文献类型：
--
作者：
R. Oliver
Jacobi三重积恒等式给出了组合学和数论中自然出现的许多无穷乘积生成函数的封闭形式。特别令人感兴趣的是它在戴德金的η-函数η（z）上的应用，η（z）是通过无穷乘积定义的，给出了某种被称为θ函数的无穷和。利用模形式的理论，我们对所有的θ函数进行了分类。
The Jacobi Triple Product Identity gives a closed form for many infinite product generating functions that arise naturally in combinatorics and number theory. Of particular interest is its application to Dedekind’s eta-function η(z), defined via an infinite product, giving it as a certain kind of infinite sum known as a theta function. Using the theory of modular forms, we classify all eta-quotients that are theta functions.