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Generalized Bernoulli numbers and congruence of modular forms
Yoshitaka Maeda
Source: Duke Math. J. Volume 57, Number 2 (1988), 673-696.
First Page PDF: View first page of article (PDF, 88 KB)Primary Subjects: 11F33
Secondary Subjects: 11S40
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077307054
Mathematical Reviews number (MathSciNet):
MR962525
Zentralblatt MATH identifier:
0664.10012
Digital Object Identifier: doi:10.1215/S0012-7094-88-05730-4
References
[1] K. Doi and T. Miyake, Automorphic Forms and Number Theory, Kinokuniya Shoten, Tokyo, 1976 (Japanese).
Zentralblatt MATH:
0466.10012
[2] B. Ferrero and R. Greenberg, On the behavior of $p$-adic $L$-functions at $s = 0$, Invent. Math. 50 (1978), no. 1, 91–102.
Mathematical Reviews (MathSciNet):
MR80f:12016
Zentralblatt MATH:
0441.12003
Digital Object Identifier: doi:10.1007/BF01406470
[3] E. Hecke, Analytische Arithmetik der positiven quadratischen Formen, Danske Vid. Selsk. Math.-Fys. Medd. 17 (1940), no. 12, 134.
Mathematical Reviews (MathSciNet):
MR2,251f
Zentralblatt MATH:
0024.00902
[4] H. Hida, Congruence of cusp forms and special values of their zeta functions, Invent. Math. 63 (1981), no. 2, 225–261.
Mathematical Reviews (MathSciNet):
MR82g:10044
Zentralblatt MATH:
0472.10028
Digital Object Identifier: doi:10.1007/BF01393877
[5] H. Hida, On congruence divisors of cusp forms as factors of the special values of their zeta functions, Invent. Math. 64 (1981), no. 2, 221–262.
Mathematical Reviews (MathSciNet):
MR83h:10066
Zentralblatt MATH:
0472.10028
Digital Object Identifier: doi:10.1007/BF01389169
[6] H. Hida, Kummer's criterion for the special values of Hecke $L$-functions of imaginary quadratic fields and congruences among cusp forms, Invent. Math. 66 (1982), no. 3, 415–459.
Mathematical Reviews (MathSciNet):
MR83j:12002
Zentralblatt MATH:
0485.10019
Digital Object Identifier: doi:10.1007/BF01389222
[7] H. Hida, Congruences of cusp forms and Hecke algebras, Séminaire de Théorie des Nombres, Paris 1983–1984, Progr. Math., vol. 59, Birkhäuser Boston, Boston, MA, 1985, pp. 133–146.
Mathematical Reviews (MathSciNet):
MR89a:11052
Zentralblatt MATH:
0575.10025
[8] H. Hida, A $p$-adic measure attached to the zeta functions associated with two elliptic modular forms I, Invent. Math. 79 (1985), no. 1, 159–195.
Mathematical Reviews (MathSciNet):
MR86m:11097
Zentralblatt MATH:
0573.10020
Digital Object Identifier: doi:10.1007/BF01388661
[9] H. Hida, Iwasawa modules attached to congruences of cusp forms, Ann. Sci. Ecole Norm. Sup. (4) 19 (1986), no. 2, 231–273.
Mathematical Reviews (MathSciNet):
MR88i:11023
Zentralblatt MATH:
0607.10022
[10] H. Hida, Galois representations into ${\mathrm GL}_ 2({\mathbf Z}_ p[[X]])$ attached to ordinary cusp forms, Invent. Math. 85 (1986), no. 3, 545–613.
Mathematical Reviews (MathSciNet):
MR87k:11049
Zentralblatt MATH:
0612.10021
Digital Object Identifier: doi:10.1007/BF01390329
[11] M. Koike, On the congruences between Eisenstein series and cusp forms, U.S.-Japan Seminar on Number Theory, Ann Arbor, 1975.
[12] K. Matter, Die den Bernoullischen Zahlen analogen Zahlen im Körper der dritten Einheitswurzeln, vol. 45, Vierteljahrsschrift Naturforschenden Gesellschaft Zürich, 1900.
Zentralblatt MATH:
31.0204.03
[13] G. Shimura, On elliptic curves with complex multiplication as factors of the jacobians of modular function fields, Nagoya Math. J. 43 (1971), 199–208.
Mathematical Reviews (MathSciNet):
MR45:5111
Zentralblatt MATH:
0225.14015
[14] H. P. F. Swinnerton-Dyer, On $\ell$-adic representations and congruences for coefficients of modular forms, Modular Functions of One variable III (Proc. Internat. Summer School, Univ. Antwerp, 1972), Lecture Notes in Math., vol. 350, Springer-Verlag, Berlin-Heidelberg-New York, 1973, pp. 1–55.
Mathematical Reviews (MathSciNet):
MR53:10717a
Zentralblatt MATH:
0267.10032
[15] M. M. Višik and Ju. I. Manin, $p$-adic Hecke series of imaginary quadratic fields, Mat. Sb. 95(137) (1974), 357–383, 471, Math. USSR-Sb. 24 (1974), 345–371.
Mathematical Reviews (MathSciNet):
MR51:8078
[16] L. C. Washington, Introduction to Cyclotomic Fields, Graduate Texts in Mathematics, vol. 83, Springer-Verlag, Berlin-Heidelberg-New York, 1982.
Mathematical Reviews (MathSciNet):
MR85g:11001
Zentralblatt MATH:
0484.12001
[17] R. I. Yager, A Kummer criterion for imaginary quadratic fields, Compositio Math. 47 (1982), no. 1, 31–42.
Mathematical Reviews (MathSciNet):
MR83k:12008
Zentralblatt MATH:
0506.12008
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