論文

1. On conjugacy classes of the pro-l braid group of degree 2, Proc. of Japan Acad., Vol. 62 Ser. A No. 7, 274--277, (1986). pdf

2. On some properties of the universal power series for Jacobi sums (with Y. Ihara and A. Yukinari), Advanced Studies in Pure Math., 12, 65--86, (1987). pdf

3. On the automorphism group of some pro-l fundamental groups (with M. Asada), Advanced Studies in Pure Math., 12, 137--159, (1987). pdf

4. On the universal power series for Jacobi sums and the Vandiver conjecture (with H. Ichimura), J. of Number Theory, 31, 312--334, (1989). pdf

5. Certain automorphism groups of pro-l fundamental groups of punctured Riemann surfaces, J. of Fac. of Sci., Univ. of Tokyo, 36, 363--372, (1989). pdf

6. Supersingular j-invariants as singular moduli mod p, Osaka J. of Math., 26, 849--855, (1989). pdf

7. A generalization of the Chowla-Selberg formula and the zeta functions of quadratic orders, Proc. of Japan Acad., Vol. 66 Ser. A No. 7, 201--203, (1990). pdf

8. Pro-l pure braid groups of Riemann surfaces and Galois representations (with Y. Ihara), Osaka J. of Math., 29, 1--19, (1992). pdf

9. Selfsimilarity in a class of quadratic-quasiperiodic chains (with T. Odagaki), J. of Phys. Soc. of Japan, 62-4, 1147--1152, (1993). pdf

10. Self-similarity of binary quasiperiodic sequences (with T. Odagaki), J. of Phys. A: Math. Gen. 27, 1683--1690, (1994). pdf

11. A Recurrence Formula for the Bernoulli Numbers, Proc. of Japan Acad. Vol. 71 Ser. A No. 8, 192--193 (1995). pdf

12. A generalized Jacobi theta function and quasimodular forms (with D. Zagier), ``The Moduli Space of Curves'', Progress in Math. 129, Birkhauser, 165--172, (1995). pdf

13. The Fourier coefficients and the singular moduli of the elliptic modular function j(tau), Mem. of Fac. Eng. and Design, Kyoto Institute of Technology 44, 1--5, (1996). pdf

14. On Ito's observation on coefficients of the modular polynomial, Proc. of Japan Acad. Vol. 72 Ser. A No. 5, 95--96, (1996). pdf

15. Zeros of certain modular functions and an application (with T. Asai and H. Ninomiya), Comment. Math. Univ. St. Pauli, 46-1, 93--101, (1997). pdf

16. Poly-Bernoulli numbers, J. de Théorie des Nombres 9, 221--228, (1997). pdf

17. Supersingular j-invariants, hypergeometric series, and Atkin's orthogonal polynomials (with D. Zagier), AMS/IP Studies in Advanced Mathematics, vol. 7, 97--126, (1998). pdf

18. Multiple zeta values, poly-Bernoulli numbers, and related zeta functions (with T. Arakawa), Nagoya Math. J., vol. 153, 189--209, (1999). pdf

19. Traces of singular moduli and the Fourier coefficients of the elliptic modular function j(tau), ``Number Theory'' (R. Gupta and K. Williams eds.), CRM Proceedings and Lecture Notes, vol. 19, 173--176, (1999). pdf

20. On Poly-Bernoulli numbers (with T. Arakawa), Comment. Math. Univ. Sanct. Pauli, vol. 48-2, 159--167, (1999). pdf

21. 素数位数を有する楕円曲線の構成とその計算量評価(with K. Horiuchi, Y. Futa, R. Sakai, and M. Kasahara), 電気情報通信学会論文誌A, Vol. J82-A, No. 8, 1269--1277, (1999). pdf

22. On the zeros of certain modular forms, ``Number Theory and its Applications '', (S. Kanemitsu and K. G\"yory eds.), Kluwer Academic Publishers, 193--197, (1999). pdf

23. The Akiyama-Tanigawa algorithm for Bernoulli numbers, Electronic J. of Integer Sequences, vol. 3, article 00.2.9, (2000). pdf

24. Hypergeometric modular forms and supersingular elliptic curves (with N. Todaka), Proceedings on Moonshine and related topics (J. Mckay and A. Sebbar ed.), CRM Proceedings and Lecture Notes, vol. 30, 79--83, (2002). pdf

25. When is a polygonal pyramid number again polygonal? (with K. Tachibana), Rockey Mountain J. of Math., vol. 32-1, 149--165, (2002). pdf

26. On modular forms arising from a differential equation of hypergeometric type (with M. Koike), The Ramanujan J., vol. 7, 145--164, (2003). pdf

27. Quasimodular forms as solutions to a differential equation of hypergeometric type (with M. Koike), Galois Theory and Modular Forms, (ed. K. Hashimoto, K. Miyake and H. Nakamura), Kluwer Academic Publishers, 329--336, (2003). pdf

28. A variation of Euler's approach to values of the Riemann zeta function (with N. Kurokawa and M. Wakayama), Kyushu J. Math., vol. 57, 175--192, (2003). pdf

29. On coefficients of Yablonskii-Vorob'ev polynomials (with H. Ochiai), J. Math. Soc. Japan, vol. 55-4, 985--993, (2003). pdf

30. The Kappa function (with M. Yoshida), Int. J. Math., vol. 14-9, 1003--1013, (2003). pdf

31. On multiple L-values (with T. Arakawa), J. Math. Soc. Japan, vol. 56-4, 967--991, (2004). pdf

32. On the local factor of the zeta function of quadratic orders, Zeta functions, Topology, and Quantum Physics, Developments in Mathematics,  Vol.14, Springer, 75--79, (2005). pdf

33. On modular forms of weight (6n+1)/5 satisfying a certain differential equation, ``Number Thoery --- Tradition and Modernization'', (Z. Wenpeng and Y. Tanigawa eds.), Kluwer, 97--102, (2006). pdf

34. Derivation and double shuffle relations for multiple zeta values (with K. Ihara and D. Zagier), Compositio Math. vol. 142-02, 307--338, (2006). pdf

35. Double zeta values and modular forms (with H. Gangl and D. Zagier), ``Automorphic forms and Zeta functions'', Proceedings of the conference in memory of Tsuneo Arakawa, World Scientific, 71--106, (2006). pdf

36. On extremal quasimodular forms (with M.Koike), Kyushu J. Math., vol. 60-2, 457--470, (2006). pdf

37. On some properties of polynomials related to hypergeometric modular forms (with N. Niiho), The Ramanujan J., 12-3, 321--325, (2006). pdf

38. On ordinary primes for modular forms and the theta operator (with M. Chida), Proc. Amer. Math. Soc. 135, 1001--1005, (2007). pdf

39. On an extension of the derivation relation for multiple zeta values, ``The Conference on L-functions'', (L. Weng and M. Kaneko eds.), World Scientific, 89--94, (2007). pdf

40. On a conjecture for the dimension of the space of the multiple zeta values (with M.Noro and K.Tsurumaki), Software for Algebraic Geometry, IMA 148, 47--58, (2008). pdf

41. A note on poly-Bernoulli numbers and multiple zeta values, Diophantine analysis and related fields (DARF 2007/2008), AIP Conf. Proc. 976, Amer. Inst. Phys., Melville, NY, 118--124, (2008). pdf

42. Ultradiscretization of a solvable two-dimensional chaotic map associated with the Hesse cubic curve (with K. Kajiwara, A. Nobe and T. Tsuda), Kyushu J. Math., vol. 63-2, 315--338, (2009). pdf

43. Observations on the 'Values' of the elliptic modular function j(tau) at real quadratics, Kyushu J. Math., vol. 63-2, 353--364, (2009). pdf

44. Poly-Bernoulli numbers and related zeta functions, ``Algebraic and Analytic Aspects of Zeta Functions and L-functions'' (Ed. by G. Bhowmik, K. Matsumoto and H. Tsumura), MSJ Memoir, vol 21, 73--85, (2010). pdf

45. On a kind of duality of multiple zeta-star values (with Y. Ohno), International Journal of Number Theory, Vol.6-8, 1927-1932, (2010) pdf

46. ECDLP への Generalized Weil Descent Attack の評価 (齋藤恆和,小林鉄太郎,山本剛 と共著), Proceedings of the 2010 Symposium on Cryptography and Information Security, Takamatsu, Japan, 1D2-3, (2010). pdf

47. Congruences modulo 4 of calibers of real quadratic fields (with K. Mori), Ann. Sci. Math. Quebec (2011) pdf

48. Elliptic curves and Fibonacci numbers arising from Lindenmayer system with Symbolic Computation (with Hiroshi Yoshida and Yoshihiro Miwa), Applicable Algebra in Engineering, Communication and Computing, Vol. 22 (2), pp. 147-164, (2011). pdf

49. On Fourier coefficients of some meromorphic modular forms (with Y. Honda), Bulletin of the Korean Mathematical Society, 49(6), p1349-1357, (2012) pdf

50. Modular Forms and Second Order Ordinary Differential Equations : Applications to Vertex Operator Algebras (with K. Nagatomo and Y. Sakai), Letters in Mathematical Physics, 103(4), p439-453, (2013) pdf

51. The Ramanujan-Serre differential operators and certain elliptic curves (with Y. Sakai) Proc. Amer. Math. Soc. 141 (2013), 3421-3429 pdf

52. Double zeta values, double Eisenstein series, and modular forms of level 2 (with K. Tasaka), Math. Ann. 367, pp 1091-1118, (2013) pdf

53. Multi-Poly-Bernoulli Numbers and Finite Multiple Zeta Values (with K. Imatomi and E. Takeda) J. of Integer Sequences. Vol. 17 (2014), Article 14.4.5. pdf

54. On multiple zeta values of extremal height (with M. Sakata), Bull. Aust. Math. Soc., 93, 186--193, (2016). pdf

55. Affine vertex operator algebras and modular linear differential equations (with Y. Arike, K. Nagatomo, and Y. Sakai), Letters in Mathematical Physics, 106 (5), 693--718, (2016) pdf

56. On the parity of calibers of real quadratic orders (with H. Sakata and M. Takeuchi), Siauliai Mathematical Seminar, 11 (19), 35--43, (2016) pdf

57. The third order modular linear differential equations (with K.~Nagatomo and Y.~Sakai), J. of Algebra, 485-1, 332--352, (2017) pdf

58. 有限多重ゼータ値(Finite multiple zeta values, in Japanese), RIMS Kôkyûroku Bessatsu B68, 175--190, (2017). pdf

59. Point-arrangements in the real projective spaces and the Fibonacci polynomials (with M. Yoshida), Kumamoto J. of Math., 31, 1 -- 13, (2018). pdf

60. On a duality formula for certain sums of values of poly-Bernoulli polynomials and its application (with F. Sakurai and H. Tsumura), J. de Théorie des Nombres de Bordeaux, 30-1, 203--218, (2018). pdf

61. A new integral-series identity of multiple zeta values and regularizations (with S. Yamamoto), Selecta Math., 24, 2499--2521, (2018). pdf

62. Multi-poly-Bernoulli numbers and related zeta functions (with H. Tsumura), Nagoya Math. J. 232, 19--54, (2018). pdf

63. Analogues of the Aoki-Ohno and Le-Murakami relations for finite multiple zeta values (with K. Oyama and S. Saito), Bull. Aust. Math. Soc., 100, 34--40, (2019). pdf

64. An introduction to classical and finite multiple zeta values, Publications Mathématiques de Besançon, 2019/1, 103--129, (2019). pdf

65. Zeta functions connecting multiple zeta values and poly-Bernoulli numbers (with H. Tsumura), Adv. Stud. Pure Math., 84, 181--204, (2020). pdf

66. Genus character L-functions of quadratic orders and class numbers (with Y. Mizuno), J. London Math. Soc., 102-1, 69--98, (2020). pdf

67. Algebraic independence results for the values of theta-constants and some identities (with C.~Elsner and Y.~Tachiya), J. Ramanujan Math. Soc., 35-1, 71--80, (2020). pdf

68. On multiple zeta vaues of level two (with H. Tsumura), Tsukuba J. Math., 44-2, 213--234, (2020). pdf

69. Quasi-derivation relations for multiple zeta values revisited (with H. Murahara and T. Murakami), Abh. Math. Semin. Univ. Hambg., 90, 151--160, (2020). pdf

70. On poly-cosecant numbers (with M. Pallewatta and H. Tsumura), J. of Integer Sequences, Vol. 23 (2020), Article 20.6.4. pdf

71. A generalized regularization theorem and Kawashima's relation for multiple zeta values (with C. Xu and S. Yamamoto), Journal of Algebra, 580, 247--263, (2021). pdf   Share Link (valid until June 05, 2021)

72. A criterion of algebraic independence of values of modular functions and an application to infinite products involving Fibonacci and Lucas numbers (with D. Duverney, C. Elsner, and Y. Tachiya), Reseach in Number Theory, 8, no. 2, Paper No. 31, 13 pp, (2022). pdf

73. A study of a Fuchsian system of rank 8 in 3 variables and the ordinary differential equations as its restrictions (with A. Ebisu, Y. Haraoka, H. Ochiai, T. Sasaki, and M. Yoshida), Osaka J. Math., 60, no. 1, 153--206, (2023). pdf

74. On finite multiple zeta values of level two (T. Murakami and A. Yoshihara), Pure and Applied Mathematics Quarterly, 19, No. 1, 267--280, (2023). pdf

75. Multiple L-values of level four, poly-Euler numbers, and related zeta functions (with H. Tsumura), to appear in Tohoku Math. J. pdf

76. Two formulas for certain double and multiple polylogarithms in two variables (with H. Tsumura), to appear in Comment. Math. Univ. Sanct. Pauli arXiv

77. Elliptic normal curves of even degree and theta functions (with M. Kuwata), to appear in Reseach in Number Theory pdf

78. On finite analogues of Euler's constant (with T. Matsusaka and S. Seki), preprint, arXiv


著書

1. ベルヌーイ数とゼータ関数 (荒川恒男, 伊吹山知義と共著), 牧野書店, (2001).

2. アイゼンシュタインとクロネッカーによる楕円関数論(A.ヴェイユ著の翻訳), シュプリンガー東京,(2005).

3. 技術に生きる現代数学(佐伯修,谷口説男,二宮嘉行,福本康秀,若山正人と共著),岩波書店,(2008).

4. 暗号の整数論(境隆一と共著),講談社サイエンティフィク,(2009).

5. Bernoulli Numbers and Zeta Functions (with T. Arakawa and T. Ibukiyama, with an appendix by D. Zagier), Springer, (2014).

6. ベルヌーイ数とゼータ関数 新装版 -- 整数論の風景 -- (荒川恒男, 伊吹山知義と共著), 共立出版, (2022).


講義録

1. 多重ゼータ値と多重ベルヌーイ数, 都立大学数学教室セミナー報告, (1997). pdf

2. 楕円モジュラー関数 j(tau) のフーリエ係数, Rokko Lectures in Mathematics 10, 神戸大学理学部数学教室, (2001). pdf

3. 多重ゼータ値入門(荒川恒男と共著), COE Lecture Note Vol. 23, 九州大学 (2010), (2016.1, 誤植,誤りを一部修正) pdf


報告集原稿など

1. E. de Shalit 「The Explicit Reciprocity Law in Local Class Field Theory」(preprint)の紹介, 数理解析研究所講究録, 589 (1986). リンク

2. Jacobi 和の universal power series と Vandiver 予想(市村文男と共同), 数理解析研究所講究録, 658(1988). リンク

3. Singular moduli と Q上の楕円曲線の supersingular prime, 数理解析研究所講究録, 721(1990). リンク

4. Supersingular j-polynomial と超幾何級数, 数理解析研究所講究録, 775(1992). リンク

5. 超特異楕円曲線と超幾何級数, 数理解析研究所講究録, 844(1993). リンク

6. Jacobi polynomials, certain elliptic modular forms and supersingular elliptic curves, 数理解析研究所講究録, 925(1995). リンク

7. 楕円曲線の j 不変量に関する話題, 第41回代数学シンポジウム報告集, (1996). pdf

8. Rademacher constant, Atkin's inner product, and zeros of elliptic modular functions, 数理解析研究所講究録, 1091(1999). リンク

9. 多重ゼータ値入門, 数理解析研究所講究録, 1097(1999). リンク

10. 多重ゼータ値の関係式について(大野泰生と共同), 第45回代数学シンポジウム報告集, (2000). pdf

11. 多重 L 値について(荒川恒男と共同), 早稲田大学整数論研究集会(2000)報告集. pdf

12. 多重ゼータ値,「数学」54巻 第4号,404--415, (2002). リンク

13. べき乗和からベルヌーイ数,ゼータ函数へ,「数学セミナー」2003年10月号, (2003). pdf

14. ある微分方程式を満たすモジュラー形式について, 数理解析研究所講究録, 1384(2004). リンク

15. いくつかのモジュラー形式の零点をめぐって, およびある微分方程式のモジュラー形式解について, 第2回保型形式周辺分野スプリングコンファレンス報告集, (2004). pdf

16. "Extremal" な準モジュラー形式について(小池正夫と共同), 早稲田大学整数論研究集会(2004)報告集. pdf

17. Double zeta values and modular forms, Japan-Korea Number Theory Seminar,2004. pdf

18. メタ・アーベル化とヤコビ和の普遍冪級数, 2004年度整数論サマースクール「基本群 と Galois 表現」報告集, (2005). pdf

19. ラマヌジャン,「数学セミナー」 2006年2月号,(2006). pdf

20. 「Gamma, Exploring Euler’s constant」(Julian Havil) の書評,「数学」58巻 第2号,213--215, (2006). pdf

21. 二重ゼータ値, 二重 Eisenstein 級数, およびモジュラー形式, 数理解析研究所講究録, 1549(2007). リンク

22. いくつかの種数 0 モジュラー関数のフーリエ係数公式(大田香織と共同),早稲田大学整数論研究集会(2007)報告集. pdf

23. セール『数論講義』,「数学セミナー」 2007年8月号,(2007). pdf

24. 多重ゼータ値と多重ベルヌーイ数, 第53回代数学シンポジウム報告集,(2008). pdf

25. IL-system-多細胞系における代数方程式=記号計算を用いた多様性パタンの解析(主著者 吉田寛), 数理解析研究所講究録, 1597(2008). リンク

26. リンデンマイヤシステム上の多細胞モデルにおける楕円曲線を含む曲線(主著者 吉田寛), 数理解析研究所講究録, 1663(2009). リンク

27. 楕円モジュラー j-関数をめぐって, 第21回草津群論セミナー(2009)報告集. pdf

28. 楕円モジュラー j 関数の実二次点での「値」とマルコフ二次無理数(繁木伸孝と共同),早稲田大学整数論研究集会(2010)報告集. pdf

29. 有限多重ゼータ値 mod p と多重ゼータ値の関係式, 数理解析研究所講究録, 1813(2012). リンク

30. アイゼンシュタインの三角関数,「数学セミナー」 2014年12月号,(2014). pdf

31. 多重ゼータ値, 第61回代数学シンポジウム,(2016). pdf

32. 分割数の漸近公式と円周法,「数学セミナー」 2017年2月号,(2017). pdf

33. 多重ゼータ値導入, 第26回整数論サマースクール,(2018). pdf

34. 「Harmonic Maass Forms and Mock Modular Forms」(Bringmann, Folsom, Ono, and Rolen) の書評,「数学」73巻 第1号,108--111, (2021). pdf

35. 「1変数保型形式の数論入門」,「数理科学」2021年2月号, (2021). pdf

36. 「科学を育む 査読の技法」(水島昇) の書評,「数学通信」27巻 第3号,123--125, (2022). pdf

37. 「多重ゼータ値」小史, 第32回数学史シンポジウム報告集(津田塾大学 数学・計算機科学研究所)に載録予定(2023). pdf

38. レベル 4 の多重 L 値について, 数理解析研究所講究録, 2238 (2023). pdf


その他

1. A Note (導分関係式の予想) (1998). pdf

2. 論文34(Ihara-Kaneko-Zagier)の前身 (20年4月に惜しくも亡くなられた高田敏恵さんの遺品の中から見つけました. うっすらと見える日付は2001年2月2日でしょうか.私自身ファイルもプリントも失っておりましたので,何かの記録になるかと,ここに置いておくことにしました.上のノートもそのついでです). pdf