研究論文一覧

  • 学位論文

    1. 修士論文:
      On a family of polynomials of $S_3$-types of the rational field (日本語)
      東京都立大学, pp.11, 1995/96.
    2. 博士論文:
      Studies in Arithmetic of Quadratic Fields Based on $S_3$-Polynomials
      東京都立大学, pp.63, Mar. 1999.

  • 査読付き雑誌に掲載された(または投稿中の)論文

    1. A criterion for a certain type of imaginary quadratic fields to have $3$-ranks of the ideal class groups greater than one
      Proc. Japan Acad. Ser. A Math. Sci. 74 (1998), no. 6, 93--97. DOI:10.3792/pjaa.74.93
    2. Parametrization of the quadratic fields whose class numbers are divisible by three (三宅克哉氏との共著)
      J. Number Theory 80 (2000), no. 2, 209--217. DOI:10.1006/jnth.1999.2455
    3. A constructive approach to Spiegelung relations between $3$-ranks of absolute ideal class groups and congruent ones modulo $(3)^2$ in quadratic fields
      J. Number Theory 83 (2000), no. 1, 1--49. DOI:10.1006/jnth.1999.2498
    4. Imaginary cyclic fields of degree $p-1$ whose relative class numbers are divisible by $p$
      Proc. Japan Acad. Ser. A Math. Sci. 77 (2001), no. 4, 55--58. DOI:10.3792/pjaa.77.55
    5. A family of cyclic cubic polynomials whose roots are systems of fundamental units
      J. Number Theory 102 (2003), no. 1, 90--106. DOI:10.1016/S0022-314X(03)00085-4;
      Erratum to "A family of cyclic cubic polynomials whose roots are systems of fundamental units" [J. Number Theory 102 (2003), no. 1, 90--106]
      J. Number Theory 103 (2003), no. 1, 132--133. DOI:10.1016/j.jnt.2003.08.001
    6. A note on the $3$-rank of quadratic fields
      Arch. Math. (Basel) 81 (2003), no. 5, 520--523. DOI:10.1007/s00013-003-4745-6
    7. On dihedral extensions and Frobenius extensions (今岡雅文氏との共著)
      in Galois theory and modular forms 195--220, Dev. Math., 11, Kluwer Acad. Publ., Boston, MA, 2004. <関連ウェブページ>
    8. On the Sylow $p$-subgroups of the ideal class groups of some imaginary cyclic fields of degree $p-1$
      Tokyo J. Math. 27 (2004), no. 2, 481--491. DOI:10.3836/tjm/1244208403
    9. The Spiegelungssatz for $p=5$ from a constructive approach
      Math. J. Okayama Univ. 47 (2005), 1--27. <関連ウェブページ>
    10. Infinite family of imaginary cyclic fields of degree $p-1$ with the $p$-rank of the ideal class groups of at least two (片山真一氏との共著)
      Tsinghua Sci. Technol. 12 (2007), no. 4, 475--478. DOI:10.1016/S1007-0214(07)70070-6
    11. A new family of imaginary quadratic fields whose class number is divisible by five
      J. Number Theory 128 (2008), no. 8, 2450--2458. DOI:10.1016/j.jnt.2008.02.016
    12. Note on the divisibility of the class number of certain imaginary quadratic fields
      Glasg. Math. J. 51 (2009), no. 1, 187--191. DOI:10.1017/S001708950800462X;
      Note on the divisibility of the class number of certain imaginary quadratic fields - Corrigendum
      Glasg. Math. J. 52 (2010), no. 1, 207--208. DOI:10.1017/S0017089509990371
    13. On $D_5$-polynomials with integer coefficients
      Ann. Math. Blaise Pascal 16 (2009), no. 1, 113--125. DOI:10.5802/ambp.258
    14. On the ideal class group of certain quadratic fields
      Glasg. Math. J. 52 (2010), no. 3, 575--581. DOI:10.1017/S0017089510000431
    15. Imaginary cyclic fields of degree $p-1$ whose ideal class groups have $p$-rank at least two
      Publ. Math. Debrecen 81 (2012), no. 3-4, 447--452. DOI:10.5486/PMD.2012.5323 <関連ウェブページ>
    16. On the $3$-rank of the ideal class group of quadratic fields
      Kodai Math. J. 36 (2013), no. 2, 275--283. DOI:10.2996/kmj/1372337518
    17. On positive integers of minimal type concerned with the continued fraction expansion (田尻彩華氏, 吉塚健一郎氏との共著)
      Math. J. Okayama Univ. 56 (2014), 35--50. <関連ウェブページ>
    18. Construction of positive integers with even period of minimal type (河本史紀氏, 冨田耕史氏との共著)
      Proc. Japan Acad. Ser. A Math. Sci. 90 (2014), no. 2, 27--32. DOI:10.3792/pjaa.90.27
    19. On systems of fundamental units of certain quartic fields (青木美穂氏との共著)
      Int. J. Number Theory 11 (2015), no. 7, 2019--2035. DOI:10.1142/S1793042115500864
    20. Continued fraction expansions with even period and primary symmetric parts with extremely large end (河本史紀氏, 冨田耕史氏との共著)
      Comm. Math. Univ. Sancti Pauli 64 (2015), no. 2, 131--155. DOI:10.14992/00011773
    21. Imaginary quadratic fields whose ideal class groups have $3$-rank at least three (小松亨氏との共著)
      J. Number Theory 170 (2017), 46--54. DOI:10.1016/j.jnt.2016.06.019
    22. A remark on the Lavallee-Spearman-Williams-Yang family of quadratic fields (Kwang-Seob Kim氏との共著)
      Math. J. Okayama Univ. 59 (2017), 113--116. <関連ウェブページ>
    23. An infinite family of pairs of imaginary quadratic fields with both class numbers divisible by five (青木美穂氏との共著)
      J. Number Theory 176 (2017), 333--343. DOI:10.1016/j.jnt.2016.12.007
    24. Divisibility of the class numbers of imaginary quadratic fields (Kalyan Chakraborty氏, Azizul Hoque氏, Prem P. Pandey氏との共著)
      J. Number Theory 185 (2018), 339--348. DOI:10.1016/j.jnt.2017.09.007
    25. Real quadratic fields, continued fractions, and a construction of primary symmetric parts of ELE type (河本史紀氏, 鈴木浩志氏, 冨田耕史氏との共著)
      Kyushu J. of Math. 73 (2019), no. 1, 165--187. DOI:10.2206/kyushujm.73.165
    26. A family of pairs of imaginary cyclic fields of degree $(p-1)/2$ with both class numbers divisible by $p$ (青木美穂氏との共著)
      Ramanujan J. 52 (2020), no. 1, 133--161. DOI:10.1007/s11139-018-0085-9
    27. $5$-class towers of cyclic quartic fields arising from quintic reflection (Abdelmalek Azizi氏, Daniel C. Mayer氏, Mohamed Talbi氏, Mohammed Talbi氏との共著)
      Ann. Math. Qué. 44 (2020), no. 2, 299--328. DOI:10.1007/s40316-019-00125-2
    28. A lower bound for the class numbers of certain real quadratic fields (河本史紀氏との共著)
      in Class Groups of Number Fields and Related Topics 43--56, Springer, Singapore, 2020. DOI:10.1007/978-981-15-1514-9_4 <関連ウェブページ>
    29. On some properties of partial quotients of the continued fraction expansion of $\sqrt{d}$ with even period (河本史紀氏, 冨田耕史氏との共著)
      Arch. Math. (Basel) 114 (2020), no. 6, 649--660. DOI:10.1007/s00013-020-01434-7
    30. Construction of families of dihedral quintic polynomials (山田芽唯氏との共著)
      Math. J. Okayama Univ. 66 (2024), 63--69. DOI:10.18926/mjou/66001
    31. Continued fractions and the class number of real quadratic orders (河本史紀氏との共著) Tokyo J. Math.に受理.
    32. On the existence of real quadratic fields with odd period of minimal type (江口喬信氏との共著) J. Korean Math. Soc.に受理
    33. On some subgroups of the ideal class group of real quadratic orders (河本史紀氏, 冨田耕史氏との共著) Kyushu J. of Math.に受理

  • 報告集など

    1. 類数が$3$で割れる二次体の特徴づけ (日本語)
      in 代数的整数論とその周辺 (日本語) 151--155, 数理解析研究所報告集 No. 1026, 1998. <関連ウェブページ>
    2. A Constructive Approach to Spiegelung-Relations between $3$-Ranks of Absolute Ideal Class Groups and Congruent Ones Modulo $3^2$ in Quadratic Fields (日本語)
      in 整数論 (日本語) 7--14, 早稲田大学研究集会報告集 No. 10, 1999.
    3. ガロアの逆問題における多項式の構成とその応用 (日本語)
      群馬法専紀要 (日本語) 14 (2000), 41--50.
    4. On imaginary cyclic fields of degree $p-1$ which have $p$-ranks of the ideal class groups greater than one (日本語)
      163--172, 早稲田大学研究集会報告集, 2002.
    5. An infinite family of imaginary cyclic fields of degree $p-1$ which have ideal class groups of $p$-ranks greater than one (片山真一氏との共著)
      in Yokoi-Chowla Conjecture and Related Problems 43--50, Proceedings of the 2003 Nagoya Conference, 2004.
    6. A constructive approach to the Spiegelungssatz for $p=5$
      in Théorie des nombres et applications 129--142, Comptes rendus de la conférence internationale Maroc-Québec 2003, 2004.
    7. Spiegelungssatzの構成的アプローチ (日本語)
      33--49, 第3回北陸数論研究集会報告集, 2005.
    8. $3$-rankが$2$以上のイデアル類群を持つ虚$2$次体の族 (日本語)
      71--80, 第8回北陸数論研究集会報告集, 2010.
    9. ある$2$次無理数の連分数展開について (日本語)
      in 計算機代数システムの進展 (日本語) 40--63, GCOEレクチャーノート報告集 Vol. 35, 2011.
    10. ある$4$次多項式と基本単数系 (日本語) (青木美穂氏との共著)
      91--107, 第9回福岡数論研究集会報告集, 2015. <関連ウェブページ>
    11. A construction of real quadratic fields of minimal type and primary symmetric parts of ELE type (河本史紀氏, 鈴木浩志氏, 冨田耕史氏との共著)
      in Algebraic Number Theory and Related Topics 2014 107--121, RIMS Kokyuroku Bessatsu, B64, 2017. <関連ウェブページ>

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Last modified: Wed., 6 Mar. 2024