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Transactions of the American Mathematical Society

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On zeta functions and Iwasawa modules

Author: Jangheon Oh
Journal: Trans. Amer. Math. Soc. 350 (1998), 3639-3655
MSC (1991): Primary 11R23
MathSciNet review: 1422616
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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.

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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

Keywords: Iwasawa module, zeta function, $p$-adic $L$-function
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 author’s Ph.D thesis. I would like to thank my adviser, W. Sinnott, for introducing me to this subject, for pointing out to me the key idea and for many valuable comments
Article copyright: © Copyright 1998 American Mathematical Society

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