On p-adic zeta functions and Z p-extensions of certain totally real number fields

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概要

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• In thes article, we describe the order of the Galois-invariant part of the p-Sylow subgroup of the ideal class group in the cyclotomic Z_p-extension of a certain totally real number field k in terms of the residue at 1 of the p-adic zeta function of k, where p denotes an odd prime number. By using this, we obtain an alternative formulation of Greenberg's theorem on the vanishing of the cyclotomic Iwasawa λ- and μ-invariants of k for p. We also give some computational data for totally real cubic fields and p=3.

• 東北大学の論文
• 1999-03-00

著者

• Taya Hisao

  Graduate School Of Information Sciences Tohoku University

関連論文

• A Note on the Iwasawa λ-Invariants of Real Abelian Number Fields
• On p-adic zeta functions and Z p-extensions of certain totally real number fields

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