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Generalizations of Iwasawa's 'Riemann-Hurwitz' Formula for Cyclic p-Extensions of Number Fields

We produce generalizations of Iwasawa's `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 λ-invariants which generalizes a result of Takashi Fukuda et. al. for totally real number fields.

preprint2013arXivOpen access
Jordan Schettler
math.NT
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Jordan Schettler

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