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Special values of L-functions attached to \(X_ 1(N)\). (English) Zbl 0519.14018

MSC:
14G10 Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture)
14H25 Arithmetic ground fields for curves
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References:
[1] B.J. Birch : Elliptic Curves, a Progress Report . Proceedings of the 1969 Summer Institute on Number Theory, Stoney Brook, New York AMS, pp. 396-400, 1971. · Zbl 0214.19801
[2] E. Friedman : Ideal class groups in basic Zp1 x ... x Zpn extensions with abelian base field . Inv. Math. 65 (1982) 425-440. · Zbl 0495.12007 · doi:10.1007/BF01396627 · eudml:142858
[3] S. Kamienny : On J1(p) and the Conjecture of Birch and Swinnerton-Dyer . Duke Math. J. 49 (1982) 329-340. · Zbl 0504.10012 · doi:10.1215/S0012-7094-82-04921-3
[4] D. Kubert and S. Lang : Modular Units , Berlin-Heidelberg -New York, Springer-Verlag, 1981. · Zbl 0492.12002
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[7] B. Mazur : On the Arithmetic of Special Values of L-functions . Inv. Math. 55 (1979) 207-240. · Zbl 0426.14009 · doi:10.1007/BF01406841 · eudml:186134
[8] H. Rademacher : Collected Papers , Volume II, Cambridge, M.I.T. Press (1974). · Zbl 0311.01022
[9] B. Schoeneberg : Elliptic Modular Functions , Springer, Grundl. d. Math. Wiss., Band 203, (1974). · Zbl 0285.10016
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[11] G. Shimura : On the Periods of Modular Forms . Math. Ann. 229 (1977) 211-221. · Zbl 0363.10019 · doi:10.1007/BF01391466 · eudml:163017
[12] L. Washington : The non-p-part of the class number in a cyclotomic Zp-extcnsion . Inv. Math. 49 (1978) 87-97. · Zbl 0403.12007 · doi:10.1007/BF01399512 · eudml:142595
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