On Ramanujan congruences between special values of Hecke and Dirichlet L-functions

• Autorzy: P. Guerzhoy
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1997
• Tom: 81
• Numer: 1
• Strony: 11-23

Daty

wydano

1997

otrzymano

1995-07-10

poprawiono

1997-02-04

Twórcy

autor

P. Guerzhoy

• Fakultät für Mathematik und Informatik, Universität Mannheim, Seminargebäude A5, D-68131 Mannheim, Germany

Bibliografia

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• [2] B. Datskovsky and P. Guerzhoy, On Ramanujan congruences for modular forms of higher weight, Proc. Amer. Math. Soc., to appear.
• [3] P. Deligne and J.-P. Serre, Formes modulaires de poids 1, Ann. Sci. Ecole Norm. Sup. 7 (1974), 507-530.
• [4] P. I. Gerzhoĭ and A. A. Panchishkin, Finiteness criterion for the number of rational points on twisted Weil elliptic curves, Zap. Nauch. Sem. LOMI 160 (1987), 41-53.
• [5] N. M. Katz, p-adic continuation of real analytic Eisenstein series, Ann. of Math. 104 (1976), 459-571.
• [6] N. Koblitz, Congruences for periods of modular forms, Duke Math. J. 54 (1987), 361-373.
• [7] N. Koblitz, p-adic congruences and modular forms of half integer weight, Math. Ann. 274 (1986), 199-220.
• [8] W. Kohnen, A simple remark on eigenvalues of Hecke operators on Siegel modular forms, Abh. Math. Sem. Univ. Hamburg 57 (1987), 33-36.
• [9] Yu. I. Manin, Periods of parabolic forms and p-adic Hecke series, Mat. Sb. 92 (1973), 378-401 (in Russian).
• [10] K. A. Ribet, Congruence relations between modular forms, in: Proceedings of the International Congress of Mathematicians (Warsaw, 1983), PWN, Warszawa, 1984, 503-514.
• [11] G. Shimura, The special values of the zeta-functions associated with cusp forms, Comm. Pure Appl. Math. 29 (1976), 783-804.
• [12] H. P. F. Swinnerton-Dyer, On l-adic representations and congruences for coefficients of modular forms, in: Modular Functions of One Variable III, Lecture Notes in Math. 350, Springer, 1973, 1-55.
• [13] H. P. F. Swinnerton-Dyer, Congruence properties of τ(n), in: Ramanujan Revisited, Proceedings of the Centenary Conference, Academic Press, 1988, 289-311.