# generalized Bernoulli number

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

 $\sum_{a=1}^{m}\chi(a)\frac{te^{at}}{e^{mt}-1}=\sum_{n=0}^{\infty}B_{n,\chi}% \frac{t^{n}}{n!}$

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

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