On zeta functions and Iwasawa modules
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Abstract:
We study the relation between zeta-functions and Iwasawa modules. We prove that the Iwasawa modules $X^{-}_{k({\zeta }_{p})}$ for almost all $p$ determine the zeta function ${\zeta }_{k}$ when $k$ is a totally real field. Conversely, we prove that the $\lambda$-part of the Iwasawa module $X_{k}$ is determined by its zeta-function ${\zeta }_{k}$ up to pseudo-isomorphism for any number field $k.$ Moreover, we prove that arithmetically equivalent CM fields have also the same ${\mu }^{-}$-invariant.References
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Additional Information
- Jangheon Oh
- Affiliation: Department of Mathematics, Ohio State University, Columbus, Ohio 43210
- Address at time of publication: KIAS, 207-43 Cheongryangri-Dong, Dongdaemun-Gu, Seoul 130-012, Korea
- Email: ohj@kias.kaist.ac.kr
- Received by editor(s): April 16, 1996
- Received by editor(s) in revised form: June 7, 1996, and October 23, 1996
- Additional Notes: This paper is part of the authorβs Ph.D thesis. I would like to thank my adviser, W.Β Sinnott, for introducing me to this subject, for pointing out to me the key idea and for many valuable comments
- © Copyright 1998 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 350 (1998), 3639-3655
- MSC (1991): Primary 11R23
- DOI: https://doi.org/10.1090/S0002-9947-98-01967-9
- MathSciNet review: 1422616