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

Abstract


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  $p.$

Keywords


Iwasawa theory, Hilbert class field, Kummer extension.

Subject classification

11R23.

Sponsor(s)



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References


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

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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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