Geodesic
Some remarks on the $l$-adic Dirichlet theorem and the $l$-adic regulator
Izvestiya. Mathematics, Tome 19 (1982) no. 3, pp. 445-478 
L. V. Kuz'min. Some remarks on the $l$-adic Dirichlet theorem and the $l$-adic regulator. Izvestiya. Mathematics, Tome 19 (1982) no. 3, pp. 445-478. http://geodesic.mathdoc.fr/item/IM2_1982_19_3_a0/
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     title = {Some remarks on the $l$-adic {Dirichlet} theorem and the $l$-adic regulator},
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] Brumer A., “On the units of algebraic number fields”, Mathematika, 14 (1967), 121–124 | MR | Zbl

[2] Ferrero B., Washington L., “The Iwasawa invariant $\mu_p$ vanishes for abelian number fields”, Ann. of Math., 109 (1979), 377–395 | DOI | MR | Zbl

[3] Iwasawa K., Lectures on $p$-adic $L$-functions, Princeton Univ. Press., 1972 | MR | Zbl

[4] Kuzmin L. V., “Modul Teita polei algebraicheskikh chisel”, Izv. AN SSSR. Ser. matem., 36:2 (1972), 267–327 | MR

[5] Kuzmin L. V., “Kogomologicheskaya razmernost nekotorykh grupp Galua”, Izv. AN SSSR. Ser. matem., 39:3 (1975), 487–495 | MR

[6] Kuzmin L. V., “Nekotorye teoremy dvoistvennosti dlya krugovykh $\Gamma$-rasshirenii polei algebraicheskikh chisel SM-tipa”, Izv. AN SSSR. Ser. matem., 43:3 (1979), 483–546 | MR

[7] Neukirch Jü., Klassenkorpertheorie, B. I-Hochschulskripten, 713/713a$^*$, Mannheim, 1969 | MR

[8] Wagstaff S., “The irregular primes to $125000$”, Math. Comp., 32 (1978), 583–591 | DOI | MR | Zbl

[9] Shafarevich I. R., $\zeta$-funktsiya, rotaprint VTs MGU, M., 1969

[10] Kokh X., Teoriya Galua $p$-rasshirenii, Mir, M., 1973 | MR