Lists of My Papers and Thesis

  • Thesis

    • Master thesis:
      On a family of polynomials of $S_3$-types of the rational field (Japanese)
      Tokyo Metropolitan University, pp.11, 1995/96.
    • Doctor thesis:
      Studies in Arithmetic of Quadratic Fields Based on $S_3$-Polynomials
      Tokyo Metropolitan University, pp.63, Mar. 1999.

  • Refereed papers

    • 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
    • Parametrization of the quadratic fields whose class numbers are divisible by three (with Katsuya Miyake)
      J. Number Theory 80 (2000), no. 2, 209--217. DOI:10.1006/jnth.1999.2455
    • 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
    • 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
    • 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
    • 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
    • On dihedral extensions and Frobenius extensions (with Masafumi Imaoka)
      in Galois theory and modular forms 195--220, Dev. Math., 11, Kluwer Acad. Publ., Boston, MA, 2004. <Web Page>
    • 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
    • The Spiegelungssatz for $p=5$ from a constructive approach
      Math. J. Okayama Univ. 47 (2005), 1--27. <Web Page>
    • Infinite family of imaginary cyclic fields of degree $p-1$ with the $p$-rank of the ideal class groups of at least two (with Shin-ichi Katayama)
      Tsinghua Sci. Technol. 12 (2007), no. 4, 475--478. DOI:10.1016/S1007-0214(07)70070-6
    • 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
    • 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
    • On $D_5$-polynomials with integer coefficients
      Ann. Math. Blaise Pascal 16 (2009), no. 1, 113--125. DOI:10.5802/ambp.258
    • On the ideal class group of certain quadratic fields
      Glasg. Math. J. 52 (2010), no. 3, 575--581. DOI:10.1017/S0017089510000431
    • 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 <Web Page>
    • 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
    • On positive integers of minimal type concerned with the continued fraction expansion (with Sayaka Tajiri and Ken-ichiro Yoshizuka)
      Math. J. Okayama Univ. 56 (2014), 35--50. <Web Page>
    • Construction of positive integers with even period of minimal type (with Fuminori Kawamoto and Koshi Tomita)
      Proc. Japan Acad. Ser. A Math. Sci. 90 (2014), no. 2, 27--32. DOI:10.3792/pjaa.90.27
    • On systems of fundamental units of certain quartic fields (with Miho Aoki)
      Int. J. Number Theory 11 (2015), no. 7, 2019--2035. DOI:10.1142/S1793042115500864
    • Continued fraction expansions with even period and primary symmetric parts with extremely large end (with Fuminori Kawamoto and Koshi Tomita)
      Comm. Math. Univ. Sancti Pauli 64 (2015), no. 2, 131--155. DOI:10.14992/00011773
    • Imaginary quadratic fields whose ideal class groups have $3$-rank at least three (with Toru Komatsu)
      J. Number Theory 170 (2017), 46--54. DOI:10.1016/j.jnt.2016.06.019
    • A remark on the Lavallee-Spearman-Williams-Yang family of quadratic fields (with Kwang-Seob Kim)
      Math. J. Okayama Univ. 59 (2017), 113--116. <Web Page>
    • An infinite family of pairs of imaginary quadratic fields with both class numbers divisible by five (with Miho Aoki)
      J. Number Theory 176 (2017), 333--343. DOI:10.1016/j.jnt.2016.12.007
    • Divisibility of the class numbers of imaginary quadratic fields (with Kalyan Chakraborty, Azizul Hoque and Prem P. Pandey)
      J. Number Theory 185 (2018), 339--348. DOI:10.1016/j.jnt.2017.09.007
    • Real quadratic fields, continued fractions, and a construction of primary symmetric parts of ELE type (with Fuminori Kawamoto, Hiroshi Suzuki and Koshi Tomita)
      Kyushu J. of Math. 73 (2019), no. 1, 165--187. DOI:10.2206/kyushujm.73.165
    • A family of pairs of imaginary cyclic fields of degree $(p-1)/2$ with both class numbers divisible by $p$ (with Miho Aoki)
      Ramanujan J. 52 (2020), no. 1, 133--161. DOI:10.1007/s11139-018-0085-9
    • $5$-class towers of cyclic quartic fields arising from quintic reflection (with Abdelmalek Azizi, Daniel C. Mayer, Mohamed Talbi, Mohammed Talbi)
      Ann. Math. Qué. 44 (2020), no. 2, 299--328. DOI:10.1007/s40316-019-00125-2
    • A lower bound for the class numbers of certain real quadratic fields (with Fuminori Kawamoto)
      in Class Groups of Number Fields and Related Topics 43--56, Springer, Singapore, 2020. DOI:10.1007/978-981-15-1514-9_4 <Web Page>
    • On some properties of partial quotients of the continued fraction expansion of $\sqrt{d}$ with even period (with Fuminori Kawamoto and Koshi Tomita)
      Arch. Math. (Basel) 114 (2020), no. 6, 649--660. DOI:10.1007/s00013-020-01434-7
    • Construction of families of dihedral quintic polynomials (with Mei Yamada)
      Math. J. Okayama Univ. 66 (2024), 63--69. DOI:10.18926/mjou/66001
    • Continued fractions and the class number of real quadratic orders (with Fuminori Kawamoto)
      to appear in Tokyo J. Math. DOI:10.3836/tjm/1502179399
    • On the existence of real quadratic fields with odd period of minimal type (with Takanobu Eguchi)
      to appear in J. Korean Math. Soc.
    • On some subgroups of the ideal class group of real quadratic orders (with Fuminori Kawamoto and Koshi Tomita)
      to appear in Kyushu J. of Math.

  • Reports or non-refereed papers

    • Characteristics of quadratic fields whose class numbers are divisible by $3$ (Japanese)
      in Algebraic Number Theory and Related Topics (Japanese) 151--155, RIMS Kokyuroku, No. 1026, 1998. <Web Page>
    • A Constructive Approach to Spiegelung-Relations between $3$-Ranks of Absolute Ideal Class Groups and Congruent Ones Modulo $3^2$ in Quadratic Fields (Japanese)
      in Number Theory (Japanese) 7--14, Proceedings of the workshop on Number Theory 1999, 1999.
    • Constructions of Polynomials for Inverse Galois Problem and its Application (Japanese)
      Gumma Hosen Kiyou (Japanese) 14 (2000), 41--50.
    • On imaginary cyclic fields of degree $p-1$ which have $p$-ranks of the ideal class groups greater than one (Japanese)
      163--172, Proceedings of the workshop on Number Theory 2002, 2002.
    • An infinite family of imaginary cyclic fields of degree $p-1$ which have ideal class groups of $p$-ranks greater than one (with Shin-ichi Katayama)
      in Yokoi-Chowla Conjecture and Related Problems 43--50, Proceedings of the 2003 Nagoya Conference, 2004.
    • 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.
    • A constructive approach to the Spiegelungssatz (Japanese)
      33--49, Proceedings of the 3rd Workshop on Number Theory, 2005.
    • A family of imaginary quadratic fields with the $3$-rank of the ideal class group at least two (Japanese)
      71--80, Proceedings of the 8th Workshop on Number Theory, 2010.
    • On continued fraction expansion of certain quadratic irrationals (Japanese)
      in Progress in Computer Algebra System (Japanese) 40--63, GCOE Lecture Note, Vol. 35, 2011.
    • Certain quartic fields and systems of fundamental units (Japanese) (with Miho Aoki)
      91--107, Proceedings of the 9th Fukuoka Symposium on Number Theory, 2015. <Web Page>
    • A construction of real quadratic fields of minimal type and primary symmetric parts of ELE type (with Fuminori Kawamoto, Hiroshi Suzuki and Koshi Tomita)
      in Algebraic Number Theory and Related Topics 2014 107--121, RIMS Kokyuroku Bessatsu, B64, 2017. <Web Page>

Back to Main Page
Last modified: Mon., 30 Apr. 2024