論文・著書等

論文リスト

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.
Self-similarity 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(τ ), 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 Th´eorie 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(τ ), "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), Rocky 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 solutions of 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. 57-1, 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 (2006), 321–325. pdf
38.
On ordinary primes for modular forms and the theta operator (with M. Chida), Proc. Amer. Math. Soc. 135 (2007), 1001-1005. 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 themultiple zeta values (with M.Noro and K.Tsurumaki), Software for Algebraic Geometry, IMA 148 (2008), 47–58. 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, 2008, 118–124. 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(τ ) 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.
Congruences modulo 4 of calibers of real quadratic fields (with K. Mori), Ann. Sci. Math. Québec (2011) pdf
47.
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
48.
Double zeta values, double Eisenstein series, and modular forms of level 2 (with K. Tasaka), preprint,(2011) pdf
49.
The Ramanujan-Serre differential operators and certain elliptic curves (with Y. Sakai), preprint, (2012) pdf
50.
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, (2010), 1D2–3 pdf
51.
On Fourier coefficients of some meromorphic modular forms (with Y. Honda), preprint, 2011 pdf

著書等

●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).
●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).
●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)．
●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).

講義録

●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).
●楕円モジュラー関数j(τ ) 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
●多重ゼータ値および多重L 値ノート，立教大学SFR 講究録No.7，(2005).
●多重ゼータ値入門(荒川恒男と共著)，九州大学MI レクチャーノート，vol. 23, (2010). pdf

その他

1. Pro-ℓ 基本群の自己同型写像について(with M. Asada), 数論研究集会報告集(長崎大学),(1986).
2. Jacobi 和のuniversal power series とVandiver 予想(with H. Ichimura), 代数的整数論研究集会報告集, 数理解析研究所講究録658, (1988). 　
3. Singular moduli とQ 上の楕円曲線のsupersingular prime, 代数的整数論研究集会報告集, 数理解析研究所講究録721, (1990). 　
4. Chowla-Selberg 　公式の一般化, 数論的代数幾何学シンポジウム報告集（東京大学), (1991).
5. Supersingular j-polynomial と超幾何級数, Einstein計量とYang-Mills接続」研究集会報告書, 数理解析研究所講究録775, (1992).
6. 超特異楕円曲線と超幾何級数, 代数的数論研究集会報告集, 数理解析研究所講究録844, (1993).　
7. 谷山－ヴェイユ予想からフェルマー予想へ, 数学セミナー1993 年9 月号.
8. Jacobi polynomials, certain elliptic modular forms and supersingular elliptic curves, 代数的整数論と数論的幾何学研究集会報告集, 数理解析研究所講究録925, (1995). 　
9. 楕円モジュラー関数j(τ ) のFourier係数とCM値, および重さ半整数のモジュラー形式, 代数群上の保型形式研究集会報告集, 数理解析研究所講究録965, (1996).
10. 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).
11. 多重ゼータ値, 多重ベルヌーイ数および関連するゼータ関数 (with T. Arakawa), 第二回津田塾大学整数論シンポジウム報告集, (1997).
12. 多重ゼータ値入門, 代数的整数論とその周辺研究集会報告集, 数理解析研究所講究録1097, (1999).
13. Rademacher contant, Atkin's inner produnt, and zeros of elliptic modular functions, 解析数論と諸分野の交流研究集会報告集, 数理解析研究所講究録1091, (1999).
14. 多重ゼータ値の関係式について(with Y. Ohno), 第45 回代数学シンポジウム報告集, (2000).
15. 多重L 値について(with T. Arakawa), 　早稲田大学整数論研究集会報告集, (2002)．
16. 多重ゼータ値，「数学」54 巻第4 号，404–415, (2002).
17. 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.
18. 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ゴンファレンス報告集, (2004). pdf
19. ある微分方程式を満たすモジュラー形式について, 解析的整数論とその周辺研究集会報告集, 数理解析研究所講究録1384, (2004).
20. 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).221–232, (16 の翻訳).
21. Multiple zeta values, Sugaku Expositions, vol. 18-2, (2005),221–232, (16 の翻訳).
22. "Extremal"な準モジュラー形式について（小池正夫氏共同）(早稲田大学整数論シンポジウム（2004.3.17--19）報告集原稿) pdf
23. 二重ゼータ値，二重 Eisenstein 級数，およびモジュラー形式，(京大数理研短期共同「多重ゼータ値の研究」（2004.11.8--11）報告集原稿) pdf