Geodesic
The $\mathfrak p$-adic zeta-fucntion of an imaginary quadratic field and the Leopoldt regualtor
Sbornik. Mathematics, Tome 31 (1977) no. 2, pp. 151-158 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

This paper gives a construction of the $\mathfrak p$-adic zeta-function of an imaginary quadratic field which can be used to express the class number with conductor $\mathfrak p^n$ of complex multiplication fields. We obtain an exact formula for the norm of the Leopoldt regulator of such fields; this formula follows from the existence of a $\Gamma$-module associated to the regulator. Bibliography: 9 titles. 
@article{SM_1977_31_2_a1,
     author = {M. M. Vishik},
     title = {The $\mathfrak p$-adic zeta-fucntion of an imaginary quadratic field and the {Leopoldt} regualtor},
     journal = {Sbornik. Mathematics},
     pages = {151--158},
     year = {1977},
     volume = {31},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1977_31_2_a1/}
}
TY  - JOUR
AU  - M. M. Vishik
TI  - The $\mathfrak p$-adic zeta-fucntion of an imaginary quadratic field and the Leopoldt regualtor
JO  - Sbornik. Mathematics
PY  - 1977
SP  - 151
EP  - 158
VL  - 31
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SM_1977_31_2_a1/
LA  - en
ID  - SM_1977_31_2_a1
ER  - 
%0 Journal Article
%A M. M. Vishik
%T The $\mathfrak p$-adic zeta-fucntion of an imaginary quadratic field and the Leopoldt regualtor
%J Sbornik. Mathematics
%D 1977
%P 151-158
%V 31
%N 2
%U http://geodesic.mathdoc.fr/item/SM_1977_31_2_a1/
%G en
%F SM_1977_31_2_a1
M. M. Vishik. The $\mathfrak p$-adic zeta-fucntion of an imaginary quadratic field and the Leopoldt regualtor. Sbornik. Mathematics, Tome 31 (1977) no. 2, pp. 151-158. http://geodesic.mathdoc.fr/item/SM_1977_31_2_a1/

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

[2] K. Iwasawa, “On $\mathbf{Z}_l$-extensions of algebraic number fields”, Ann. Math., 98:2 (1973), 246–326 | DOI | MR | Zbl

[3] H. W. Leopoldt, “Zur Arithmetik in abelschen Zahlkörpern”, J. reine und angew. Math., 209 (1962), 54–71 | MR | Zbl

[4] Yu. I. Manin, “Periody parabolicheskikh form i $p$-adicheskie ryady Gekke”, Matem. sb., 92 (134) (1973), 376–401 | MR

[5] K. Ramachandra, “Some applications of Kronecker's limit formulas”, Ann. Math., 80:1 (1964), 104–148 | DOI | MR | Zbl

[6] G. Robert, “Unités Elliptiques”, Bull. Soc. Math. Françe, Suppl., 1973, no. 36 | MR

[7] C. L. Siegel, Lectures on Advanced Analytic Number Theory, Tata Institut, Bombay, 1961 | MR

[8] M. M. Vishik, “Nearkhimedovy mery, svyazannye s ryadami Dirikhle”, Matem. sb., 99(141) (1976), 248–260 | Zbl

[9] B. Mazur, “$p$-Adic Analytic Number Theory of Elliptic Curves and Abelian Varieties over $\mathbf{Q}$”, Proc. Int. Congr. of Math., Vancouver, 1974, 369–377 | MR