Publications

Books (in Japanese)
・ 理工系新課程 線形代数 基礎から応用まで 培風館,2004 (共著)

・新しい視点からの線形代数 培風館,1998 (共著)
 
Papers
[27] N.Ishii, Minimal equations and values of generalized lambda functios, arXiv:1504.05272v2[math.NT] 25 Nov 2015.

[26] N,Ishii,Generalized lambda functions and modular function fields of principal congruence subgroups, Tokyo J. Math. 37 (2014) ,NO. 1, 237-246.

[25] N.Ishii,Special values of generalized lambda functions at imagainary quadratic points, Ramanujan J.33 (2014),121-130,DOI 10.1007/s11139-013-9463-5.

[24] N.Ishii,M.Kobayashi, Singular values of some modular functions, Ramanujan J. 24 No.1 (2011),67-83,DOI 10.1007/s11139-010-9249-y.

[23] S.Yoshimura, A.Comuta, N.Ishii, Modular equation of a function field with respect to a group Γ_0(4p),  Far East Journal of Mathematical Sciences 36 (2) (2010),101-124.

[22] S.Yoshimura, A.Comuta, N.Ishii, N-systems,class polynomials of double eta-quotients and singular values of j-invariant function, Int.Math.Forum 4(2009) no.8,367-376.

[21] N.Ishii, Rational expression for J-invariant function in terms of generators of modular function fields, Int.Math. Forum 2 (2007) no. 38, 1877 - 1894. 

[20] N.Ishii, Trace of Frobenius endomorphism of an elliptic curve with Complex multiplication, Bulletin of Australian Math.Soc. 70 (2004) 125--142.

[19] N.Ishida, N. Ishii, Generators and defining equation of the modular function field of the group Γ_1(N), Acta Arith.101.4 (2002),303-320.

[18] N.Ishida, N. Ishii, The equation for the modular curve X_1(N) derived from the equation for the modular curve X(N), Tokyo J.Math.22 (1999),no. 1, 167-175.

[17] N.Ishida, N. Ishii, The equations for modular function fields of principal congruence subgroups of prime level. Manuscripta Math. 90 (1996), no. 3, 271--285.

[16] N.Ishii, Defining equations of modular function fields. Math. Japon. 38 (1993), no. 5, 941--951.

[15] N.Ishii, P. Kaplan, K.S. Williams, On Eisenstein's problem. Acta Arith. 54 (1990), no. 4, 323--345.

[14] F.Halter-Koch, N. Ishii, Ring class fields modulo 8 of Q() and the quartic character of units of Q() for m≡1 mod 8. Osaka J. Math. 26 (1989), no. 3, 625--646.

[13] N.Ishii, Quadratic units and congruences between Hilbert modular forms. Investigations in number theory, 261--275, Adv. Stud. Pure Math., 13, Academic Press, Boston, MA, 1988.

[12] N.Ishii, On the eighth power residue of totally positive quadratic units. Investigations in number theory, 413--431, Adv. Stud. Pure Math., 13, Academic Press, Boston, MA, 1988.

[11] Y.Chuman, N. Ishii, On the quartic residue of quadratic units of negative norm. Math. Japon. 32 (1987), no. 3, 389--420.

[10] T.Hiramatsu, N. Ishii, Y. Mimura, On indefinite modular forms of weight one. J. Math. Soc. Japan 38 (1986), no. 1, 67--83.

[9] T.Hiramatsu, N. Ishii, Corrections to: "Quartic residuacity and cusp forms of weight one". Comment. Math. Univ. St. Paul. 35 (1986), no. 1, 111.

[8] T.Hiramatsu, N.Ishii, Quartic residuacity and cusp forms of weight one. Comment. Math. Univ. St. Paul. 34 (1985), no. 1, 91--103.

[7] N.Ishii, On the quartic residue symbol of totally positive quadratic units. Tokyo J. Math. 9 (1986), no. 1, 53--65.

[6] N.Ishii, Cusp forms of weight one, quartic reciprocity and elliptic curves. Nagoya Math. J. 98 (1985), 117--137.

[5] N.Ishii, Construction of generators of modular function fields. Math. Japon. 28 (1983), no. 6, 655--681
.
[4] N.Ishii, Rational points on canonical models of principal congruence subgroups. Math. Sem. Notes Kobe Univ. 8 (1980), no. 1, 187--197.

[3] N.Ishii, Modular curves and Diophantine equations. Math. Japon. 25 (1980), no. 2, 245--250.

[2] N.Ishii, An application of the Fricke formula for quaternion groups. Collection of articles dedicated to Tatsujiro Shimizu on the occasion of his 77th birthday. Math. Japon. 20 (1975), special issue, 171--177.

[1] N.Ishii, Fricke formula for quaternion groups. Proc. Japan Acad. 50 (1974), 677--682.

Preprints


                                    
[1] 
N.Ishii, Families of cyclic groups of large order obtained from the elliptic curve with CM-8,DMIS-RR-01-1,2001.      Download