On the factors of the jacobian variety of a modular function field

Goro SHIMURA

doi:10.2969/jmsj/02530523

Goro SHIMURA

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JOURNAL FREE ACCESS

1973 Volume 25 Issue 3 Pages 523-544

DOI https://doi.org/10.2969/jmsj/02530523

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Published: 1973 Received: November 13, 1972 Available on J-STAGE: September 29, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: September 29, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) A. O. L. Atkin and J. Lehner, Hecke operators on Γ₀(m), Math. Ann., 185 (1970), 134-160.
2) W. Casselman, On some results of Atkin and Lehner, to appear.
3) W. L. Chow, On the quotient variety of an abelian variety, Proc. Nat. Acad. Sci. U. S. A., 38 (1952), 1039-1044.
4) E. Hecke, Über ein Fundamentalproblem aus der Theorie der elliptischen Modulfunktionen, Abh. Math. Sem. Hamburg, 6 (1928), 235-257 (=Math. Werke, 525-547).
5) E. Hecke, Über das Verhalten der Integrale 1. Gattung bei Abbildungen, insbesondere in der Theorie der elliptischen Modulfunktionen, Abh. Math. Sem. Hamburg, 8 (1930), 271-281 (=Math. Werke, 548-558).
6) H. Jacquet and R. P. Langlands, Automorphic forms on GL(2), Lecture notes in mathematics, 114, Springer, 1970.
7) H. Jacquet, Automorphic forms on GL(2), Part II, Lecture notes in mathematics, 278, Springer, 1972.
8) T. Miyake, On automorphic forms on GL₂ and Hecke operators, Ann. of Math., 94 (1971), 174-189.
9) A. P. Ogg, On a convolution of L-series, Invent, math., 7 (1969), 297-312.
10) R. A. Rankin, Contributions to the theory of Ramanujan's functionτ(n) and similar arithmetical functions I, II, Proc. Cambridge Phil. Soc., 35 (1939), 351-372.
11) G. Shimura, Introduction to the arithmetic theory of automorphic functions, Publ. Math. Soc. Japan, No. 11, Iwanami Shoten and Princeton University Press, 1971.
12) G. Shimura, On elliptic curves with complex multiplication as factors of the jacobians of modular function fields, Nagoya Math. J., 43 (1971), 199-208.
13) G. Shimura, Class fields over real quadratic fields and Hecke operators, Ann. of Math., 95 (1972), 130-190.
14) G. Shimura, On modular forms of half integral weight, Ann. of Math, 97 (1973), 440-481.
15) A. Weil, Variétés abéliennes et courbes algébriques, Hermann, Paris, 1948.
16) A. Weil, Über die Bestimmung Dirichletscher Reihen durch Funktionalgleichungen, Math. Ann., 168 (1967), 149-156.
17) A. Weil, Dirichlet series and automorphic forms, Lecture notes in mathematics, 189, Springer, 1971.

Right : [1] A. O. L. Atkin and J. Lehner, Hecke operators on Γ₀(m), Math. Ann., 185 (1970), 134-160.
[2] W. Casselman, On some results of Atkin and Lehner, to appear.
[3] W. -L. Chow, On the quotient variety of an abelian variety, Proc. Nat. Acad. Sci. U. S. A., 38 (1952), 1039-1044.
[4] E. Hecke, Über ein Fundamentalproblem aus der Theorie der elliptischen Modulfunktionen, Abh. Math. Sem. Hamburg, 6 (1928), 235-257 (=Math. Werke, 525-547).
[5] E. Hecke, Über das Verhalten der Integrale 1. Gattung bei Abbildungen, insbesondere in der Theorie der elliptischen Modulfunktionen, Abh. Math. Sem. Hamburg, 8 (1930), 271-281 (=Math. Werke, 548-558).
[6] H. Jacquet and R. P. Langlands, Automorphic forms on GL(2), Lecture notes in mathematics, 114, Springer, 1970.
[7] H. Jacquet, Automorphic forms on GL(2), Part II, Lecture notes in mathematics, 278, Springer, 1972.
[8] T. Miyake, On automorphic forms on GL₂ and Hecke operators, Ann. of Math., 94 (1971), 174-189.
[9] A. P. Ogg, On a convolution of L-series, Invent, math., 7 (1969), 297-312.
[10] R. A. Rankin, Contributions to the theory of Ramanujan's functionτ(n) and similar arithmetical functions I, II, Proc. Cambridge Phil. Soc., 35 (1939), 351-372.
[11] G. Shimura, Introduction to the arithmetic theory of automorphic functions, Publ. Math. Soc. Japan, No. 11, Iwanami Shoten and Princeton University Press, 1971.
[12] G. Shimura, On elliptic curves with complex multiplication as factors of the jacobians of modular function fields, Nagoya Math. J., 43 (1971), 199-208.
[13] G. Shimura, Class fields over real quadratic fields and Hecke operators, Ann. of Math., 95 (1972), 130-190.
[14] G. Shimura, On modular forms of half integral weight, Ann. of Math, 97 (1973), 440-481.
[15] A. Weil, Variétés abéliennes et courbes algébriques, Hermann, Paris, 1948.
[16] A. Weil, Über die Bestimmung Dirichletscher Reihen durch Funktionalgleichungen, Math. Ann., 168 (1967), 149-156.
[17] A. Weil, Dirichlet series and automorphic forms, Lecture notes in mathematics, 189, Springer, 1971.

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