generalized Bernoulli number

Let $\chi$ be a non-trivial primitive character mod $m$. The generalized Bernoulli numbers $B_{n,\chi }$ are given by

$$\sum _{a=1}^m\chi (a)\frac{t{e}^{at}}{e^{mt}-1}=\sum _{n=0}^{\mathrm{\infty }}{B}_{n,\chi }\frac{t^n}{n!}$$

They are members of the field $\mathbb{Q}(\chi )$ generated by the values of $\chi$.

Title	generalized Bernoulli number
Canonical name	GeneralizedBernoulliNumber
Date of creation	2013-03-22 13:22:40
Last modified on	2013-03-22 13:22:40
Owner	sucrose (1410)
Last modified by	sucrose (1410)
Numerical id	6
Author	sucrose (1410)
Entry type	Definition
Classification	msc 11B68
Related topic	BernoulliNumber