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We prove that if a subfield of the Hilbert class field of an imaginary quadratic field $k$ meets the anticyclotomic ${\mathbb Z}_{p}$-extension $k_{\infty}^{a}$ of $k$, then it is contained in $k_{\infty}^{a}$ . And we give an example of an imaginay quadratic field $k$ with $\lambda_{3}(k_{\infty}^{a}) \geq 8.$
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참고문헌 (6)
참고문헌 신청
J.Minardi / 1986 / Iwasawa modules for Zdp -extensions of algebraic number elds / 박사 / University of Washington
J.Oh / 2007 / On the rst layer of anti-cyclotomic Zp-extension over imaginary qua-dratic elds / Proc. Japan Acad. Ser.A Math.Sci 83 (3) : 19 ~ 20
J.Oh / 2010 / Construction of 3-Hilbert class eld of certain imaginary quadratic elds / Proc. Japan Aca. Ser.A Math. Sci 86 (1) : 18 ~ 19
Jangheon Oh / 2009 / A note on the first layers of Z_{p}-extensions / 대한수학회논문집 24 (1) : 1 ~ 4
S.Fujii / 2013 / On a bound of and the vanishing of of Zp-extensions of an imaginary quadratic eld / J.Math.Soc.Japan 65 (1) : 277 ~ 298
J.Oh / 2007 / On the rst layer of anti-cyclotomic Zp-extension over imaginary qua-dratic elds / Proc. Japan Acad. Ser.A Math.Sci 83 (3) : 19 ~ 20
J.Oh / 2010 / Construction of 3-Hilbert class eld of certain imaginary quadratic elds / Proc. Japan Aca. Ser.A Math. Sci 86 (1) : 18 ~ 19
Jangheon Oh / 2009 / A note on the first layers of Z_{p}-extensions / 대한수학회논문집 24 (1) : 1 ~ 4
S.Fujii / 2013 / On a bound of and the vanishing of of Zp-extensions of an imaginary quadratic eld / J.Math.Soc.Japan 65 (1) : 277 ~ 298
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