志賀 弘典 (Hironori Shiga)
専攻分野
- 複素多様体論、多変数保型形式論、超幾何微分方程式論とその数論的応用。
とくにこれらの分野を横断するテーマとして楕円モジュラー函数の多変数的拡張
とその数論的応用を目指している。
論文
- Shiga, Hironori; Appendix: Periods on the Kummer surface. Algebra nd number theory, 356--358, Hindustan Book Agency, Delhi, 2005.
- Shiga, Hironori; Tsutsui, Toru; Wolfart, J¥"urgen Triangle
Fuchsian differential equations with apparent singularities. With
an appendix by Paula B. Cohen. Osaka J. Math. 41 (2004), no. 3,
625--658.
- Narumiya, Norihiko; Shiga, Hironori The mirror map for a family
of $K3$ surfaces induced from the simplest 3-dimensional reflexive
polytope. Proceedings on Moonshine and related topics (Montr¥'eal, QC,
1999), 139--161, CRM Proc. Lecture Notes, 30
(2001), Amer. Math. Soc.
- Koike, K.; Shiga, H.; Takayama, N.; Tsutsui, T. Study on the
family of $K3$ surfaces induced from the lattice $(D\sb 4)\sp 3\oplus
\langle-2\rangle\oplus\langle 2\rangle$. Internat. J. Math. 12
(2001), no. 9, 1049--1085.
- Narumiya, Norihiko; Shiga, Hironori On certain rational cuboid
problems. Nihonkai Math. J. 12 (2001), no. 1, 75--88.
- Kitazume, Masaaki; Koike, Kenji; Shiga, Hironori Notes on a
certain integral orthogonal group and its quotient by the principal
congruence subgroup of level 2. Kyushu J. Math. 54 (2000), no. 2,
257--271.
- Shiga, Hironori On the arithmetic properties of the modular
function induced from the hypergeometric differential equation of
type $(3,6)$. Proceedings of the Seventh International Colloquium on
Differential Equations (Plovdiv, 1996), 381--388, VSP, Utrecht, 1997.
- Shiga, Hironori An elaborate adaptation of a famous poem as a
mathematical technique. (Japanese) S\=ugaku 48 (1996), no. 4, 400--414.
- Shiga, Hironori; Wolfart, J¥"urgen Criteria for complex
multiplication and transcendence properties of automorphic
functions. J. Reine Angew. Math. 463 (1995), 1--25.
- Shiga, Hironori On the transcendency of the values of the
modular function at algebraic points. Journ¥'ees Arithm¥'etiques,
1991 (Geneva). Ast¥'erisque No. 209 (1992),
16, 293--305.
- Shiga, Hironori On the representation of the Picard modular
function by $\theta$ constants. I, II. Publ. Res. Inst. Math. Sci. 24 1988), no. 3, 311--360.
- Shiga, Hironori On the algebraicity of the ratio of special theta onstants. Tokyo J. Math. 11 (1988), no. 1, 81--84.
- Shiga, Hironori On $K3$ modular functions. (Japanese) Sugaku
Expositions 1 (1988), no. 2, 195--217. S\=ugaku 38 (1986), no. 2,
116--132.
- Shiga, Hironori One attempt to the $K3$ modular function. II.
Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 8 (1981), no. 1, 157--182.
- Shiga, Hironori One attempt to the $K3$ modular function $I$.
Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 6 (1979), no. 4, 609--635.
- Shiga, Hironori On the automorphism of $C\sp{2}$ with invariant
axes. J. Math. Soc. Japan 29 (1977), no. 3, 529--535.
- Shiga, Hironori On the pair of functions on $C\sp{2}$ reduced to
a pair of rational functions. J. Math. Kyoto Univ. 15 (1975), 231--236.
- Shiga, Hironori On the parametrization of a family of analytic
sets defined by an open holomorphic mapping. Sci. Papers College Gen. d. Univ. Tokyo 22 (1972), 103--112.
著書および訳書
- １５週で学ぶ複素関数論、数学書房(2006)
- 数学おもちゃ箱、日本評論社（1999）
- 数学の領域、日本評論社(1995)
- フェルマーの系譜、日本評論社(1994)
（Scharlau and Opolka 著 “From Fermat to Minkowski” の翻訳）
所属： 千葉大学 理学部 数学・情報数理学科
電話： 043-290-2727，
FAX： 043-290-2733
電子メール： shiga AT math.s.chiba-u.ac.jp
居室： 理学部2号館 5階 502
住所： 〒263-8522 千葉市 稲毛区 弥生町 1-33