On elliptic modular surfaces
ジャーナル
フリー
1972 年 24 巻 1 号 p. 20-59
詳細
- Published: 1972 Received: 1971/03/01 Available on J-STAGE: 2006/09/29 Accepted: - Advance online publication: - Revised: -
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訂正情報
訂正日: 2006/09/29 訂正理由: - 訂正箇所: 引用文献情報 訂正内容: Wrong : 1) J. W. S. Cassels, Diophantine equations with special reference to elliptic curves, J. London Math. Soc., 41 (1966), 193-291.
2) P. Deligne, Formes modulaires et représentations 1-adiques, Sém. Bourbaki, Fév. 1969, exp. 355, 1-33.
3) M. Eichler, Eine Verallgemeinerung der Abelschen Integrale, Math. Z., 67 (1957), 267-298.
4) E. Hecke, Mathematische Werke, Göttingen, 1959 (esp. No. 36 (1937), 672-707; No. 41 (1940), 789-918).
5) J. Igusa, Fibre systems of Jacobian varieties (III. Fibre systems of elliptic curves), Amer. J. Math., 81 (1959), 453-476.
6) J. Igusa, Kroneckerian model of fields of elliptic modular functions, Amer. J. Math., 81 (1959), 561-577.
7) J. Igusa, Modular forms and projective invariants, Amer. J. Math., 89 (1967), 817-855.
8) Y. Ihara, Hecke polynomials as congruence ζ functions in elliptic modular case, Ann. of Math., 85(1967), 267-295.
9) Y. Ihara, On congruence monodromy problems I, II, Lecture notes, Univ. of Tokyo, 1968-69.
10) Y. Kawada, Theory of automorphic functions of one variable I, II, Lecture notes, Univ. of Tokyo, 1963-64, (in Japanese).
11) K. Kodaira, On compact analytic surfaces II-III, Ann. of Math., 77 (1963), 563-626; 78 (1963), 1-40, (cited as K)).
12) K. Kodaira, On the structure of compact complex analytic surfaces, I, Amer. J. Math., 86 (1964), 751-798.
13) M. Kuga and I. Satake, Abelian varieties attached to polarized K3-surfaces, Math. Ann., 169 (1967), 239-242; 173 (1967), 322.
14) M. Kuga and G. Shimura, On the zeta function of a fibre variety whose fibres are abelian varieties, Ann. of Math., 82 (1965), 478-539.
15) S. Lang, Diophantine geometry, Intersc. Tracts, No. 11, 1962.
16) Y. Morita, Hecke polynomials of modular groups and congruence zeta functions of fibre varieties, J. Math. Soc. Japan, 21 (1969), 607-637.
17) A. Néron, Modèles minimaux des variétés abéliennes sur les corps locaux etglobaux, Publ. I. H. E. S., No. 21, 1964.
18) A. P. Ogg, Cohomology of abelian varieties over function fields, Ann. of Math., 76 (1962), 185-212.
19) A. P. Ogg, Elliptic curves and wild ramification, Amer. J. Math., 89 (1967), 1-21.
20) I. R. Šafarevic, Principal homogeneous spaces defined over a function field, Amer. Math. Soc. Trans., (2), 37 (1964), 85-114.
21) H. Shimizu, On traces of Hecke operators, J. Fac. Sci. Univ. of Tokyo, Sec. I, 10 (1963), 1-19.
22) G. Shimura, Sur les intégrales attachées aux formes automorphes, J. Math. Soc. Japan, 11 (1959), 291-311, (cited as S)).
23) G. Shimura, Correspondances modulaires et les functions ζ de courbes algébriques, J. Math. Soc. Japan, 10 (1958), 1-28.
24) T. Shioda, Elliptic modular surfaces, I, II, Proc. Japan Acad., 45 (1969), 786-790, 833-837.
25) B. Schoeneberg, Über den Zusammenhang der Eissensteinschen Reihen and Thetareihen mit der Diskriminante der elliptischen Funktionen, Math. Ann., 126 (1953), 177-184.
26) J. Tate, Algebraic cycles and poles of zeta functions, Arithmetical Algebraic Geometry, Harpar and Row, 1965, p. 93-110.
27) J. Tate, On the conjecture of Birch and Swinnerton-Dyer and a geometric analog, Sém. Bourbaki, Fév. 1966, exp. 306, 1-26.
28) A. Weil, Basic number theory, Springer, New York, 1967.
29) G. Shimura, Introduction to the arithmetic theory of automorphic functions, Publ. Math. Soc. Japan 11, 1971.
Right : [1] J. W. S. Cassels, Diophantine equations with special reference to elliptic curves, J. London Math. Soc., 41 (1966), 193-291.
[2] P. Deligne, Formes modulaires et représentations 1-adiques, Sém. Bourbaki, Fév. 1969, exp. 355, 1-33.
[3] M. Eichler, Eine Verallgemeinerung der Abelschen Integrale, Math. Z., 67 (1957), 267-298.
[4] E. Hecke, Mathematische Werke, Göttingen, 1959 (esp. No. 36 (1937), 672-707; No. 41 (1940), 789-918).
[5] J. Igusa, Fibre systems of Jacobian varieties (III. Fibre systems of elliptic curves), Amer. J. Math., 81 (1959), 453-476.
[6] J. Igusa, Kroneckerian model of fields of elliptic modular functions, Amer. J. Math., 81 (1959), 561-577.
[7] J. Igusa, Modular forms and projective invariants, Amer. J. Math., 89 (1967), 817-855.
[8] Y. Ihara, Hecke polynomials as congruence ζ functions in elliptic modular case, Ann. of Math., 85 (1967), 267-295.
[9] Y. Ihara, On congruence monodromy problems I, II, Lecture notes, Univ. of Tokyo, 1968-69.
[10] Y. Kawada, Theory of automorphic functions of one variable I, II, Lecture notes, Univ. of Tokyo, 1963-64, (in Japanese).
[11] K. Kodaira, On compact analytic surfaces II-III, Ann. of Math., 77 (1963), 563-626; 78 (1963), 1-40, (cited as [K]).
[12] K. Kodaira, On the structure of compact complex analytic surfaces, I, Amer. J. Math., 86 (1964), 751-798.
[13] M. Kuga and I. Satake, Abelian varieties attached to polarized K3-surfaces, Math. Ann., 169 (1967), 239-242; 173 (1967), 322.
[14] M. Kuga and G. Shimura, On the zeta function of a fibre variety whose fibres are abelian varieties, Ann. of Math., 82 (1965), 478-539.
[15] S. Lang, Diophantine geometry, Intersc. Tracts, No. 11, 1962.
[16] Y. Morita, Hecke polynomials of modular groups and congruence zeta functions of fibre varieties, J. Math. Soc. Japan, 21 (1969), 607-637.
[17] A. Néron, Modèles minimaux des variétés abéliennes sur les corps locaux et globaux, Publ. I. H. E. S., No. 21, 1964.
[18] A. P. Ogg, Cohomology of abelian varieties over function fields, Ann. of Math., 76 (1962), 185-212.
[19] A. P. Ogg, Elliptic curves and wild ramification, Amer. J. Math., 89 (1967), 1-21.
[20] I. R. Šafarevic, Principal homogeneous spaces defined over a function field, Amer. Math. Soc. Trans., (2), 37 (1964), 85-114.
[21] H. Shimizu, On traces of Hecke operators, J. Fac. Sci. Univ. of Tokyo, Sec. I, 10 (1963), 1-19.
[22] G. Shimura, Sur les intégrales attachées aux formes automorphes, J. Math. Soc. Japan, 11 (1959), 291-311, (cited as [S]).
[23] G. Shimura, Correspondances modulaires et les functions ζ de courbes algébriques, J. Math. Soc. Japan, 10 (1958), 1-28.
[24] T. Shioda, Elliptic modular surfaces, I, II, Proc. Japan Acad., 45 (1969), 786-790, 833-837.
[25] B. Schoeneberg, Über den Zusammenhang der Eissensteinschen Reihen and Thetareihen mit der Diskriminante der elliptischen Funktionen, Math. Ann., 126 (1953), 177-184.
[26] J. Tate, Algebraic cycles and poles of zeta functions, Arithmetical Algebraic Geometry, Harpar and Row, 1965, p. 93-110.
[27] J. Tate, On the conjecture of Birch and Swinnerton-Dyer and a geometric analog, Sém. Bourbaki, Fév. 1966, exp. 306, 1-26.
[28] A. Weil, Basic number theory, Springer, New York, 1967.
[29] G. Shimura, Introduction to the arithmetic theory of automorphic functions, Publ. Math. Soc. Japan 11, 1971.
訂正日: 2006/09/29 訂正理由: - 訂正箇所: PDFファイル 訂正内容: -
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