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Mat. Sb. (N.S.), 1977, Volume 102(144), Number 2, Pages 173–181 (Mi msb2644)  

The $\mathfrak p$-adic zeta-fucntion of an imaginary quadratic field and the Leopoldt regualtor

M. M. Vishik


Abstract: 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.

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English version:
Mathematics of the USSR-Sbornik, 1977, 31:2, 151–158

Bibliographic databases:

UDC: 511.61
MSC: Primary 12B30, 14B20; Secondary 12A25
Received: 19.04.1976

Citation: M. M. Vishik, “The $\mathfrak p$-adic zeta-fucntion of an imaginary quadratic field and the Leopoldt regualtor”, Mat. Sb. (N.S.), 102(144):2 (1977), 173–181; Math. USSR-Sb., 31:2 (1977), 151–158

Citation in format AMSBIB
\Bibitem{Vis77}
\by M.~M.~Vishik
\paper The $\mathfrak p$-adic zeta-fucntion of an imaginary quadratic field and the Leopoldt regualtor
\jour Mat. Sb. (N.S.)
\yr 1977
\vol 102(144)
\issue 2
\pages 173--181
\mathnet{http://mi.mathnet.ru/msb2644}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=480435}
\zmath{https://zbmath.org/?q=an:0443.12007}
\transl
\jour Math. USSR-Sb.
\yr 1977
\vol 31
\issue 2
\pages 151--158
\crossref{https://doi.org/10.1070/SM1977v031n02ABEH002295}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1977FY72200002}


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