L. V. Kuz'min, “Some remarks on the $l$-adic Dirichlet theorem and the $l$-adic regulator”, Math. USSR-Izv., 19:3 (1982), 445

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Mathematics of the USSR-Izvestiya, 1982, Volume 19, Issue 3, Pages 445–478
DOI: https://doi.org/10.1070/IM1982v019n03ABEH001424 (Mi im1712)

This article is cited in 9 scientific papers (total in 9 papers)

Some remarks on the $l$-adic Dirichlet theorem and the $l$-adic regulator

L. V. Kuz'min

English version PDF (1762 kB) Citations (9) Russian version article

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DOI: https://doi.org/10.1070/IM1982v019n03ABEH001424

Abstract: The Leopoldt conjecture is proved for some special types of nonabelian number fields. A new definition of the $l$-adic regulator is proposed, which makes sense for any algebraic number field, and in some special cases it is proved that this regulator is different from zero. In addition, estimates are obtained for the rank of the matrix figuring in the definition of the regulator.
Bibliography: 10 titles.

Received: 14.04.1981

Bibliographic databases:

UDC: 519.4

MSC: Primary 12B10, 12B45; Secondary 12B25, 12B20

Language: English

Original paper language: Russian

Citation: L. V. Kuz'min, “Some remarks on the $l$-adic Dirichlet theorem and the $l$-adic regulator”, Math. USSR-Izv., 19:3 (1982), 445–478

Citation in format AMSBIB

\Bibitem{Kuz81}

\by L.~V.~Kuz'min

\paper Some remarks on the $l$-adic Dirichlet theorem and the $l$-adic regulator

\jour Math. USSR-Izv.

\yr 1982

\vol 19

\issue 3

\pages 445--478

\mathnet{http://mi.mathnet.ru//eng/im1712}

\crossref{https://doi.org/10.1070/IM1982v019n03ABEH001424}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=641800}

\zmath{https://zbmath.org/?q=an:0527.12012}

Linking options:

https://www.mathnet.ru/eng/im1712

https://doi.org/10.1070/IM1982v019n03ABEH001424

https://www.mathnet.ru/eng/im/v45/i6/p1203

Cycle of papers

Some remarks on the $l$-adic Dirichlet theorem and the $l$-adic regulator
L. V. Kuz'min
Izv. Akad. Nauk SSSR Ser. Mat., 1981, 45:6, 1203–1240
Some remarks on the $l$-adic regulator. II
L. V. Kuz'min
Izv. Akad. Nauk SSSR Ser. Mat., 1989, 53:4, 782–813
Some remarks on the $\ell$-adic regulator. III
L. V. Kuz'min
Izv. RAN. Ser. Mat., 1999, 63:6, 29–82
Some remarks on the $\ell$-adic regulator. IV
L. V. Kuz'min
Izv. RAN. Ser. Mat., 2000, 64:2, 43–88
Some remarks on the $\ell$-adic regulator. V. Growth of the $\ell$-adic regulator in the cyclotomic $Z_\ell$-extension of an algebraic number field
L. V. Kuz'min
Izv. RAN. Ser. Mat., 2009, 73:5, 105–170

This publication is cited in the following 9 articles:

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Известия Академии наук СССР. Серия математическая

Statistics & downloads:
Abstract page:	278
Russian version PDF:	85
English version PDF:	14
References:	53
First page:	2

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