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. 47 (2024), no. 1, 245--280. DOI:10.3836/tjm/1502179399
    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. 61 (2024), no. 4, 779--796. DOI:10.4134/JKMS.j230527
    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. 78 (2024), no. 2, 433--485. DOI:10.2206/kyushujm.78.433
    34. On a theorem of Lu (河本史紀氏との共著) (投稿中)

  • 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: Fri., 10 Jan. 2025