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Congruences between cusp forms and linear representations of the Galois group*)

Published online by Cambridge University Press:  22 January 2016

Masao Koike
Masao Koike*
Affiliation:
Nagoya University
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Let f(z) be a cusp form of type (l,ε) on Γ0(N) which is a common eigenfunction of all Hecke operators. For such f(z), Deligne and Serre [1] proved that there exists a linear representation

such that the Artin L-function for p is equal to the L-function associated to f(z).

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 64 , December 1976 , pp. 63 - 85
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1976

Footnotes

*)

This work was partially supported by the Sakkokai Foundation.

References

[1] Deligne, P. and Serre, J.-P., Formes modulaires de poids 1, Anscientn.. Éc. Norm. Sup. 4e série, t. 7 (1974), 507–530.Google Scholar
[2] Dickson, L. E., Linear groups with an exposition of the Galois field theory, Leipzig, Teubner, 1901.Google Scholar
[3] Doi, K. and Yamauchi, M., On the Hecke operators for Γ0(N) and class fields over quadratic number fields, J. Math. Soc. Japan, 25 (1973), 629–643.Google Scholar
[4] Hecke, E., Theorie der Eisensteinschen Reihen höherer Stufe und ihre Anwendung auf Funktionen théorie und Arithmetik, Math. Werke, 461–486.Google Scholar
[5] Iwasawa, K. and Sims, C. C., Computation of invariants in the theory of cyclotomic fields, J. Math. Soc. Japan, 18 (1966), 86–96.Google Scholar
[6] Serre, J.-P., Propriétés galoisiennes des points d’ordre fini des courbes elliptiques, Inventiones math., 15 (1972), 259–331.CrossRefGoogle Scholar
[7] Serre, J.-P., Formes modulaires et fonction zêta p-adique, Modular functions of one variable III, Proc. Intern. Summer School, Univ. Antwerp, 1972, Springer Lecture Notes in Mathematics No. 350, 191–268.Google Scholar
[8] Shimura, G., Class fields over real quadratic fields and Hecke operators, Ann. of Math., 95 (1972), 130–190.Google Scholar
[9] Asai, T., On the Fourier coefficients of automorphic forms at various cusps and some applications to Rankin’s convolution, J. Math. Soc. Japan, 28 (1976), 48–61.Google Scholar
[10] Stickelberger, L., Über eine Verallgemeinerung der Kreistheilung, Math. Ann., 37 (1890), 321–367.Google Scholar