Divisibility Properties of the Fourier Coefficients of the Modular Invariant j(τ)
Divisibility Properties of the Fourier Coefficients of the Modular Invariant j(τ)
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模不变量 j(τ) 的傅里叶系数的整除性质
DOI：
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发表时间：
1949
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通讯作者：
J. Lehner
中科院分区：
文献类型：
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作者：
J. Lehner
证明这一定理背后的一般思想如下。以同余(1.2)为例。将用u5-表示的某一线性算子应用于(1.1)的右元，得到用5v代替v的级数。对左侧构件执行的相同操作产生属于全模组的子组的模函数。因此，我们将尝试用子群的基函数来表示模函数，子群的基函数已知具有整系数傅立叶展开。由此产生的同一性具有以下形式
The general idea behind the proof of this theorem is as follows. Consider the congruence (1. 2) as an example. By applying a certain linear operatordenoted by U5-to the right member of (1. 1) one obtains the series with v replaced by 5v. The same operation performed on the left member yields a modular function belonging to a subgroup of the full modular group. We shall try, therefore, to express that modular function in terms of the basic function of the subgroup, which is known to have integral coefficient Fourier expansions. The identity which results is of the form