Arithmetic interpretation of class number formulae
The class number formulae of the last section have been studied by several authors, for instance Robert (1973), Kersey (1980), Nakamula (1981–1985), Hayashi (1983–1986), Hajir (1993), and Limmer (1994). In this chapter we follow and refine the ideas of Schertz(1974, 1977, 1978). The aim is to express the product of the A(χ) in (11.6), up to a factor cL, as the regulator of a unit group U0 in L generated by elliptic units. Then (11.6) can be read as index formula
in which the unit group E of L and the index [E : U0] has to be understood as the index of the corresponding subgroups in the logarithmic ...