Korean J. Math.  Vol 26, No 2 (2018)  pp.293-297
DOI: https://doi.org/10.11568/kjm.2018.26.2.293

Construction of the Hilbert class field of some imaginary quadratic fields

Jangheon Oh


In the paper [4], we constructed $3$-part of the Hilbert class field of imaginary quadratic fields whose class number is divisible exactly by $3.$ In this paper, we extend the result for any odd prime  $p.$


Iwasawa theory, Hilbert class field, Kummer extension.

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H.Cohen, Advanced Topics in Computational Number Theory, Springer, 1999. (Google Scholar)

J.Minardi, Iwasawa modules for Zdp-extensions of algebraic number fields, Ph.D dissertation, University of Washington, 1986. (Google Scholar)

J.Oh, On the first layer of anti-cyclotomic Zp-extension of imaginary quadratic fields, Proc. of The Japan Acad. Ser.A 83 (2007) (3),19–20. (Google Scholar)

J.Oh, Construction of 3-Hilbert class field of certain imaginary quadratic fields, Proc. of The Japan Acad. Ser.A 86 (2010) (1), 18–19. (Google Scholar)

L.Washington, Introduction to cyclotomic fields, Springer, New York, 1982. (Google Scholar)


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