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generalized Bernoulli number (Definition)

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

$\displaystyle \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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See Also: Bernoulli number
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Cross-references: generated by, field, primitive character
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This is version 3 of generalized Bernoulli number, born on 2003-01-20, modified 2003-01-20.
Object id is 3910, canonical name is GeneralizedBernoulliNumber.
Accessed 2411 times total.

Classification:
AMS MSC: 11B68 (Number theory :: Sequences and sets :: Bernoulli and Euler numbers and polynomials)
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