References
Birch, B.J.: Elliptic curves, a progress report. Proceedings of the 1969 Summer Institute on Number Theory, Stoney Brook, New York AMS, pp. 396–400, 1971
Cassels, J.W.S., Fröhlich, A.: Algebraic Number Theory. London-New York: Academic Press 1967
Deligne, P., Rapoport, M.: Schémas de modules des courbes elliptiques. Vol. II of the Proceedings of the International Summer School on modular functions, Antwerp (1972). Lecture Notes in Mathematics349. Berlin-Heidelberg-New York: Springer 1973
Ferrero, B., Greenberg, R.: On the behavior ofp-acidL-functions ats=0. Invent. Math.,50, 91–102 (1978)
Ferrero, B., Washington, L.: The Iwasawa invariantμ p vanishes for abelian number fields. Annals of Math.,109, 377–395 (1979)
Goldfeld, D., Viola, C.: Mean values ofL-functions associated to elliptic, Fermat and other curves at the centre of the critical strip. In press (1979)
Grothendieck, A.: Modèles de Néron et monodromie exp IX. Lecture Notes in Mathematics288, Berlin-Heidelberg-New York: Springer 1972
Manin, Y.: Parabolic points and zeta functions of modular forms [in Russian], Izv. Akad. Nauk. CCCP,36, 19–65 (1972)
Mazur, B.: Courbes elliptiques et symboles modulaires. Séminaire Bourbaki, No. 414, Lecture Notes in Mathematics, No.317, Berlin-Heidelberg-New York: Springer 1973
Mazur, B.: Rational points on abelian varieties with values in towers of number fields, Inventiones Math.,18, 183–266 (1972)
Mazur, B.: Rational points on modular curves. Proceedings of a conference on modular functions held in Bonn 1976. Lecture Notes in Math.,601, Berlin-Heidelberg-New York: Springer 1977
Mazur, B.: Modular curves and the Eisenstein ideal. Publ. Math. I.H.E.S.47, 33–189 (1977)
Mazur, B.: Rational Isogenies of Prime Degree. Inventiones Math.,14, 129–162 (1978)
Mazur, B., Swinnerton-Dyer, P.: Arithmetic of Weil curves. Inventiones Math.25, 1–61 (1974)
Rademacher, H.: Topics in Analytic Number Theory. Berlin-Heidelberg-New York: Springer 1973
Rademacher, H.: Collected Papers, Volume I, Cambridge: M.I.T. Press 1974
Schoeneberg, B.: Elliptic Modular Functions. New York-Heidelberg-Berlin: Springer-Verlag 1974
Serre, J-P., Tate, J.: Good reduction of abelian varieties, Ann. of Math.88, 492–517 (1968)
Shimura, G.: Introduction to the arithmetic theory of automorphic functions. Publ. Math. Soc. Japan, No.11, Tokyo-Princeton, 1971
Washington, L.C.: Class numbers andZ p -extensions. Math. Ann.214, 177–193 (1975)
Washington, L.: The nonp-part of the class number in a cyclotomicZ p -extension. Invent. Math.,49, 87–97 (1978)
Wiles, A.: On modular curves and the class group ofQ(ζ p ). Inventiones Math., in press (1979)
Author information
Authors and Affiliations
Additional information
Much of this paper was written while I was visiting the Institut des Hautes Etudes Scientifiques and the Collége de France. I greatly appreciate their warm hospitality and congenial atmosphere
Rights and permissions
About this article
Cite this article
Mazur, B. On the arithmetic of special values ofL functions. Invent Math 55, 207–240 (1979). https://doi.org/10.1007/BF01406841
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01406841