The $\mathfrak p$-adic zeta-fucntion of an imaginary quadratic field and the Leopoldt regualtor

This paper gives a construction of the $\mathfrak p$-adic zeta-function of an imaginary quadratic field which can be used to express the class number with conductor $\mathfrak p^n$ of complex multiplication fields.
We obtain an exact formula for the norm of the Leopoldt regulator of such fields; this formula follows from the existence of a $\Gamma$-module associated to the regulator.
Bibliography: 9 titles.