On a new type of $\ell$-adic regulator for algebraic number fields. II
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L. V. Kuz′min
Translated by: the author - St. Petersburg Math. J. 27 (2016), 977-984
- DOI: https://doi.org/10.1090/spmj/1430
- Published electronically: September 30, 2016
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Abstract:
In a preceding paper of the author, a new type of an $\ell$-adic regulator $\mathfrak R_\ell (K)$ was introduced for an algebraic number field $K$ such that the prime $\ell$ splits completely in $K$. Nevertheless, the element $\mathfrak R_\ell (K)\in \mathbb Z_\ell$ is defined only up to an arbitrary factor in $(\mathbb Z_\ell ^\times )^2$. In the present paper, under the assumption of the validity of the Shanuel conjecture (both Archimedean and $\ell$-adic), the definition of $\mathfrak R_\ell (K)$ as a certain number in $\mathbb Z_\ell$ is given. For a real quadratic field $K$, such a defition can be obtained without using any additional conjectures.References
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Bibliographic Information
- L. V. Kuz′min
- Affiliation: National Research Center “Kurchatovskii Institute”, Akad. Kurchatov Sq. 1, 123182 Moscow, Russia
- Email: lvkuzmin@mail.ru
- Received by editor(s): June 25, 2015
- Published electronically: September 30, 2016
- Additional Notes: The author was supported by RFBR (grant no. 14-01-00393)
- © Copyright 2016 American Mathematical Society
- Journal: St. Petersburg Math. J. 27 (2016), 977-984
- MSC (2010): Primary 11R04
- DOI: https://doi.org/10.1090/spmj/1430
- MathSciNet review: 3589226
Dedicated: Dedicated to S. V. Vostokov on the occasion of his 70th anniversary.