On Certain Multiple Series with Functional Equation in a Totally Real Number Field II
On Certain Multiple Series with Functional Equation in a Totally Real Number Field II
This is a continuation of the preceding paper [3] with the same title.We shall treat the series with ' 'fractional powers" (see (1. 1) below), which is a generalization ofthe series $\sum_{n=1}^{\infty}\sum_{m=1}^{\infty}\frac{1}{n}e^{-2\pi m^{k}n\tau}$ $(\tau>0)$ .Let $K$ be a totally real number field of degree $n$ and $K^{\langle q)}(q=1, \cdots, n)$ …