Correspondances modulaires et les fonctions ζ de courbes algébriques

Gorô SHIMURA

doi:10.2969/jmsj/01010001

Gorô SHIMURA

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JOURNAL FREE ACCESS

1958 Volume 10 Issue 1 Pages 1-28

DOI https://doi.org/10.2969/jmsj/01010001

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Published: 1958 Received: November 05, 1957 Available on J-STAGE: August 29, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: August 29, 2006 Reason for correction: - Correction: TITLE Details: Wrong : Correspondances modulaires et les fonctions ζ de courbes algebriques
Right : Correspondances modulaires et les fonctions ζ de courbes algébriques

Date of correction: August 29, 2006 Reason for correction: - Correction: AUTHOR Details: Wrong : Par Goro SHIMURA
Right : Gorô SHIMURA¹⁾

Date of correction: August 29, 2006 Reason for correction: - Correction: AFFILIATION Details: Right :
1) Université de Tokyo

Date of correction: August 29, 2006 Reason for correction: - Correction: CITATION Details: Right : [1] W. L. Chow, The jacobian variety of an algebraic curve, Amer. J. Math., 76 (1954), pp. 453-476.
[2] M. Deuring, Die Typen der Multiplikatorenringe elliptischer Funktionenkörper, Abh. Math. Sem. Univ. Hamburg, 14 (1941), pp. 197-272.
[3] M. Eichler, Quaternäre quadratische Formen und die Riemannsche Vermutung für die Kongruenzzetafunktion, Arch. Math., 5 (1954), pp. 355-366.
[4] E. Hecke, Über die Modulfunktionen und die Dirichletschen Reihen mit Eulerschen Produktentwicklung I, II, Math. Ann., 114 (1937), pp. 1-28, 316-351.
[5] G. Shimura, Reduction of algebraic varieties with respect to a discrete valuation of the basic field, Amer. J. Math., 77 (1955), pp. 134-176.
[6] G. Shimura, On complex multiplications, Proc. International Symposium on algebraic number theory, Tokyo-Nikko, (1955), pp. 23-30.
[7] Taniyama, Jacobian varieties and number fields, Proc. International Symposium on algebraic number theory, Tokyo-Nikko, (1955). pp. 31-45.
[8] G. Shimura et Y. Taniyama, Complex multiplication of abelian varieties and its applications to number theory, à paraître dans J. Math. Soc. Japan.
[9] A. Weil, Foundations of algebraic geometry, New York, (1946).
[10] A. Weil, Sur les courbes algébriques et les variétés qui s'en déduisent, Paris, (1948).
[11] A. Weil, Variétés abéliennes et courbes algébriques, Paris, (1948).
[12] A. Weil, On algebraic groups and homogeneous spaces, Amer. J. Math., 77 (1955), pp. 493-512.

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