Research Keywords 【 display / non-display

  • class number, unit group, abelian extension, class number formula, Iwasawa theory

Research Pursuits 【 display / non-display

  • Let p be an odd prime, and let B denote the unique abelian extension over the rational field, contained in the complex field, whose Galois group over the rational field is topologically isomorphic to the additive group of p-adic integers. The p-class group of B is known to be trivial by Iwasawa. Let l be an odd prime different from p. The question whether the l-class group of B is trivial has been considered in our previous papers mainly for the case where l varies with p fixed. We gave a criterion, for checking the triviality of the l-class group of B, which enables us to discuss the triviality when p varies with l fixed. Moreover, discussing the sufficient condition with the help of a personal computer, we found that, if l does not exceed 13 and p does not exceed 101, then the l-class group of B is trivial. Although our numerical result is thus limited, our criterion for checking the triviality of the l-class group of B seems to be widely applicable. As to the 2-class group of B, we have already given in a sufficient condition for its triviality on previous papers.

Campus Career 【 display / non-display

  • Graduate School of Humanities and Sciences, Research Organization, the Core Section The Natural/Applied Sciences Division, Lecturer

  • Faculty of Core Research Natural Science Division, Lecturer

  • Graduate School of Humanities and Sciences, Education Organization, Doctral Program Advanced Sciences

  • Graduate School of Humanities and Sciences, Education Organization, Doctral Program Advanced Sciences

  • Graduate School of Humanities and Sciences, Education Organization, Master's Program Advanced Sciences

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Papers 【 display / non-display

  • Non-norm-Euclidean fields in basic Z_l-extensions

    Proceedings of the Japan Academy, Series A, vol.92(1)(p.23 - 26), 2016.01, HORIE Mitsuko・HORIE Kuniaki, Original, Research paper (scientific journal), Capital Author

  • The l-class group of the Z_p-extension over the rationals

    Journal of the Mathematical Society of Japan, vol.64(4)(p.1071 - 1089), 2012.10, HORIE Mitsuko, HORIE Kuniaki, Original, Research paper (scientific journal), Capital Author

  • The narrow class groups of the Z_17- and Z_19 extensions over the rational field

    Abh. Math. Sem. Univ. Hamburg, 2010.06, Mitsuko Horie and Kuniaki Horie, Original, Research paper (scientific journal), Capital Author

  • The ideal class group of the Z_23-extension over the rational field

    Proc. Japan Acad. Ser. A, 2009.12, Mitsuko Horie and Kuniaki Horie, Original, Research paper (scientific journal), Capital Author

  • The ideal class group of the Zp-extension over the rationals

    Tohoku Math. J., 2009.11, Mitsuko Horie and Kiuniaki Horie, Original, Research paper (scientific journal), Capital Author

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Published Article 【 display / non-display

  • Cho, Peter J.; Kim, Henry H. Dihedral and cyclic extensions with large class numbers

    Mathematical Reviews, 2013.07, HORIE Mitsuko, Survey, Single Author, Except for reviews, Book review and document introduction, etc.

  • Fouvry, Etiennne; Kluners, Jurgen On the Spielungssats for the 4-rank

    Mathematical Reviews, 2011.02, HORIE Mitsuko, Survey, Single Author, Except for reviews, Book review and document introduction, etc.

  • Li, Wei; Zhang, Xian Ke Parametrization of the quadratic fields whose divisor class number s are divisible by three

    Mathematical Revuews, 2009.10, HORIE Mitsuko, Survey, Single Author, Except for reviews, Book review and document introduction, etc.

  • Spearman, Blair K.; Monogenic A_4 quartic fields

    Mathematical Reviews, 2007.06, HORIE Mitsuko, Survey, Single Author, Except for reviews, Book review and document introduction, etc.

  • Lavallee, Melissa J.; Spearman, Blair K.; Williams, Kenneth S.; Yang, Qiduan Dihedral quintic fields with a power basis

    Mathematical review, 2006, Mitsuko Horie, Other article

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Presentations 【 display / non-display

  • On the narrow class groups of the Z_p-extensions over Q for several primes p

    Mitsuko Horie and Kuniaki Horie, Domestic, 2010.03, Joint Workshop on Number Theory between Japan and Taiwan 2010, Waseda University, Waseda University, Invited, Coauthor

  • On the narrow class group of the Z_p-extension over the rationals

    Mituko Horie and Kuniaki Horie, Domestic, 2008.03, Workshop on Number Theory 2008, Ohkubo Campus, Waseda University, Institute of Pure and Applied Mathematics, Waseda University, Invited, Coauthor

  • On number knots

    Mitsuko Horie and Kuniaki Horie, Domestic, 2004.01, 第2回北陸数論研究集会, 金沢大学サテライトプラザ, Invited, Main Speaker

  • 素数次巡回拡大の絶対類体の number knot

    堀江 充子, Domestic, 1999.09, 第5回津田塾大学整数論シンポジウム, 津田塾大学, 津田塾大学 数学・計算機科学研究所, Invited, Main Speaker

  • 類構造に関する一注意

    堀江 充子、堀江 邦明, Domestic, 1997.09, 日本数学会, 東京大学, 日本数学会, Not Invited, Coauthor

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