Generalizations of Iwasawas Riemann-Hurwitz Formula for Cyclic p-Extensions of Number Fields

We produce generalizations of Iwasawas `Riemann-Hurwitz formula for number fields. These generalizations apply to cyclic extensions of number fields of degree p^n for any positive integer n. We first deduce some congruences and inequalities and then use these formulas to establish a vanishing criterion for Iwasawa \lambda-invariants which generalizes a result of Takashi Fukuda et. al. for totally real number fields.

Author: Jordan Schettler

Source: https://archive.org/