[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.11568/kjm.2018.26.2.293

CONSTRUCTION OF THE HILBERT CLASS FIELD OF SOME IMAGINARY QUADRATIC FIELDS

Oh, Jangheon (Faculty of Mathematics and Statistics Sejong University)

Publication Information

Korean Journal of Mathematics / v.26, no.2, 2018 , pp. 293-297 More about this Journal

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;

Citations & Related Records

Reference

1	H.Cohen, Advanced Topics in Computational Number Theory, Springer, 1999.
2	J.Minardi, Iwasawa modules for $\mathbb{Z}_p^d$ -extensions of algebraic number ﬁelds, Ph.D dissertation, University of Washington, 1986.
3	J.Oh, On the ﬁrst layer of anti-cyclotomic $\mathbb{Z}_p$ -extension of imaginary quadratic ﬁelds, Proc. of The Japan Acad. Ser.A 83 (2007) (3),19-20. DOI
4	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. DOI
5	L.Washington, Introduction to cyclotomic ﬁelds, Springer, New York, 1982.