In this note, we prove an asymptotic formula for the mean-square of the so-called periodic zeta-function with respect to the parameter. This may be compared with similar formulae for Dirichlet L-functions to (multiplicative) residue class characters due to Paley and others. The periodic zeta-function is the twist of the Riemann zeta-function with an additive character.

中文翻译：

---

加性扭曲的离散矩。I：均方

在这篇笔记中，我们证明了所谓的周期 zeta 函数关于参数的均方的渐近公式。由于佩利和其他人，这可以与狄利克雷 L 函数到（乘法）残基类字符的类似公式进行比较。周期 zeta 函数是具有加性特征的黎曼 zeta 函数的扭曲。