References
Barsky, D.: Fonctions zêtap-adiques d'une classe de rayon des corps totalement réels. Groupe d'étude d'analyse ultramétrique 1977–78; errata, 1978–79
Cassou-Noguès, P.: Valeurs aux entiers négatifs des fonctions zêta et fonctions zêtap-adiques. Invent. Math.51, 29–59 (1979)
Coates, J.:p-adicL-functions and Iwasawa's theory. In: Algebraic Number Fields (A. Fröhlich, ed.). London-New York-San Francisco: Academic Press 1977
Deligne, P.: Variétés abéliennes ordinaires sur un corps fini. Invent. Math.8, 238–243 (1969)
Deligne, P.: Letters to J-P. Serre: October, 1972 and December, 1973
Deligne, P., Rapoport, M.: Les schémas de modules de courbes elliptiques. Lecture Notes in Math.349, 143–316 (1973)
Eichler, M.: On theta functions of real algebraic number fields. Acta Arith.33, 269–292 (1977)
Gelbart, S.: Weil's representation and the spectrum of the metaplectic group. Lecture Notes in Math.530, 1976
Hecke, E.: Mathematische Werke. Göttingen: Vandenhoeck und Ruprecht 1959
Hirzebruch, F.: Hilbert modular surfaces. Enseignement Math.19, 183–281 (1973)
Hurwitz, A.: Mathematische Werke. Basel: Emil Birkhäuser 1932
Igusa, J.: On the algebraic theory of elliptic modular functions. J. Math. Soc. Japan20, 96–106 (1968)
Iwasawa, K.: Lectures onp-adicL-functions. Princeton: Princeton University Press 1972
Jacquet, H., Langlands, R.P.: Automorphic forms onGL(2). Lectures Notes in Math114 (1970)
Katz, N.:p-adic properties of modular schemes and modular forms. Lecture Notes in Math.350, 70–190 (1973)
Katz, N.: The Eisenstein measure andp-adic interpolation. Amer. J. Math.99, 238–311 (1977)
Katz, N.:p-adicL-functions via moduli of elliptic curves. Proc. Symp. Pure Math.29, 479–506 (1975)
Katz, N.:p-adic interpolation of real analytic Eisenstein series. Ann. of Math.104, 459–571 (1976)
Katz, N.:p-adicL-functions forCM fields. Invent. Math.49, 199–297 (1978)
Koblitz, N.:p-adic numbers,p-adic analysis, and Zeta-Functions. New York-Heidelberg-Berlin: Springer-Verlag 1977
Kubert, D., Lang, S.: Units in the modular function field. Lecture Notes in Math.601, 247–275 (1977)
Lang, S.: Algebraic Number Theory. Reading, Mass.: Addison-Wesley 1970
Lang, S.: Introduction to Modular Forms. Berlin-Heidelberg-New York: Springer-Verlag 1976
Lang, S.: Cyclotomic Fields. Berlin-Heidelberg-New York: Springer-Verlag 1978
Mazur, B.: Analysep-adique. Unpublished manuscript, 1973
Mazur, B., Swinnerton-Dyer, H.P.F.: Arithmetic of Weil Curves. Invent. Math.25, 1–61 (1974)
Queen, C.: The existence ofp-adicL-functions. Number Theory and Algebra, pp. 263–288. New York: Academic Press 1977
Rapoport, M.: Compactifications de l'espace de modules de Hilbert-Blumenthal. Compositio Math.36, 255–335 (1978)
Ribet, K.:p-adic interpolation via Hilbert modular forms. Proc. Symp. Pure Math.29, 581–592 (1975)
Ribet, K.: Report onp-adicL-functions over totally real fields. Astérisque61, 177–192 (1979)
Sato, M., Shintani, T.: On zeta functions associated with prehomogeneous vector spaces. Ann. of Math.100, 131–170 (1974)
Serre, J-P.: Abelianl-adic representations and elliptic curves. New York: Benjamin 1968
Serre, J-P.: Formes modulaires et fonctions zêtap-adiques. Lecture Notes in Math.350, 191–268 (1973)
Serre, J-P.: Sur le résidu de la fonction zêtap-adique d'un corps de nombres. C.R. Acad. Sci. Paris287, Série A, 183–188 (1978)
Shimizu, H.: Theta series and automorphic forms onGL 2. J. Math. Soc. Japan24, 638–683 (1972). (Correction: J. Math. Soc. Japan26, 374–376 (1974))
Shintani, T.: On construction of holomorphic cusp forms of half integral weight. Nagoya Math. J.58, 83–126 (1975)
Shintani, T.: On evaluation of zeta functions of totally real algebraic number fields at non-positive integers. J. Fac. Sci. Univ. Tokyo Sect. IA23, 393–417 (1976)
Siegel, C.L.: Über die Fourierschen Koeffizienten von Modulformen. Gött. Nach.3, 15–56 (1970)
Tate, J.: Fourier analysis in number fields and Hecke's zeta-functions. Algebraic Number Theory (J.W.S. Cassels and A. Fröhlich, eds.) London-New York: Academic Press 1967
Weil, A.: Fonction zêta et distributions. Séminaire Bourbaki 312, Juin, 1966 (=Collected Papers [1966])
Weil, A.: Sur certains groupes d'opérateurs unitaires. Acta Math.111, 143–211 (1964) (=Collected Papers [1964b])
Whittaker, E.T., Watson, G.N.: A Course of Modern Analysis. Fourth edition, reprinted. Cambridge: Cambridge University Press 1935
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Deligne, P., Ribet, K.A. Values of abelianL-functions at negative integers over totally real fields. Invent Math 59, 227–286 (1980). https://doi.org/10.1007/BF01453237
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DOI: https://doi.org/10.1007/BF01453237