Generalizations of Iwasawa's 'Riemann-Hurwitz' Formula for Cyclic p-Extensions of Number Fields
Abstract
We produce generalizations of Iwasawa's `Riemann-Hurwitz' formula for number fields. These generalizations apply to cyclic extensions of number fields of degree pn for any positive integer n. We first deduce some congruences and inequalities and then use these formulas to establish a vanishing criterion for Iwasawa λ-invariants which generalizes a result of Takashi Fukuda et. al. for totally real number fields.
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