Higher relative class number formulae

@article{Kolster2002HigherRC,
  title={Higher relative class number formulae},
  author={Manfred Kolster},
  journal={Mathematische Annalen},
  year={2002},
  volume={323},
  pages={667-692}
}
Abstract. Let E be a totally complex abelian number field with maximal real subfield F, and let $\chi$ denote the non-trivial character of $Gal (E/F)$. Similar to the classical case n=1 the value of the Artin L-function $L(E/F,\chi,1-n)$ at $1-n$ for odd $n \geq 3$ is given by a relative class number formula of the form $L(E/F,\chi,1-n) = \pm \frac{2^{r_1+1}}{Q_n} \cdot \frac{h_n^{ -}}{w_n(E)}.$ Here $r_1 = [F:{\Bbb Q}], w_n(E) = |H^0(E,{\Bbb Q}/{\Bbb Z}(n))|, Q_n$ is a higher Q-index… CONTINUE READING