Lichtenbaum, Stephen On p-adic L-functions associated to elliptic curves. (English) Zbl 0425.12017 Invent. Math. 56, 19-55 (1980). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 3 ReviewsCited in 15 Documents MSC: 11S40 Zeta functions and \(L\)-functions 14H25 Arithmetic ground fields for curves 14K22 Complex multiplication and abelian varieties 14H52 Elliptic curves Keywords:evaluation of p-adic L-functions; elliptic curve; complex multiplication; imaginary quadratic number field; Iwasawa functions PDF BibTeX XML Cite \textit{S. Lichtenbaum}, Invent. Math. 56, 19--55 (1980; Zbl 0425.12017) Full Text: DOI EuDML References: [1] Coates, J., Wiles, A.: Kummer’s criterion for Hurwitz numbers. Proceedings of the International Congress on Algebraic Number Theory, Japan: Kyoto 1976 · Zbl 0369.12009 [2] Coates, J., Wiles, A.: On the conjecture of Birch and Swinnerton-Dyer, Invent. math.39, 223-251 (1977) · Zbl 0359.14009 · doi:10.1007/BF01402975 [3] Honda, T.: Formal groups and zeta-functions, Osaka J. Math.5, 199-213 (1968). · Zbl 0169.37601 [4] Hurwitz, A.: Über die Entwicklungskoeffizienten der lemniscatischen Funktionen. Math. Ann.51, 196-226 (1899) · JFM 29.0385.02 · doi:10.1007/BF01453637 [5] Iwasawa, K.: Lectures onp-adicL-functions, Ann. of Math. Studies 74, Princeton Univ. Press, 1972 [6] Katz, N.: The Eisenstein measure andp-adic interpolation, Amer. J. Math.99, 238-311 (1977) · Zbl 0375.12022 · doi:10.2307/2373821 [7] Katz, N.:P-adic interpolation of real analytic Eisenstein series, Annals of Math.104, 459-571 (1976) · Zbl 0354.14007 · doi:10.2307/1970966 [8] Lang, S., Elliptic Functions, Reading, Mass. Addison-Wesley, 1973 · Zbl 0316.14001 [9] Leopoldt, H.W.: Einep-adische Theorie der Zetawerte II, Z. Reine Ang. Math.274/75, 224-239 (1975) · Zbl 0309.12009 · doi:10.1515/crll.1975.274-275.224 [10] Manin, J., Vishik, S.:p-adic Hecke series for quadratic imaginary fields. Math. Sbornik V.95, 137 (1974) · Zbl 0329.12016 [11] Ramachandra, K.: Some applications of Kronecker’s limit formulas, Ann. of Math. No.80, 104-148 (1964) · Zbl 0142.29804 · doi:10.2307/1970494 [12] Robert, G.: Unités elliptiques et formules pour le nombre de classes des extensions abéliennes d’un corps quadratique imaginaire, Bull. Soc. Math. France, Mémoire36, 1974 [13] Robert, G.: Régularité des ideaux premiers d’un corps quadratique imaginaire de nombre de classes un, asterisque,24/25, 75-79 (1975) · Zbl 0318.12003 [14] Serre, J.-P.: Formes modulaires et fonctions zetap-adiques. Proceedings of the 1972 Antwerp Summer School, Springer Lecture notes in Mathematics350, 191-268 (1973) [15] Siegel, C.L.: Lecture notes on advanced analytic number theory, Tata Inst. of Fund. Research, Bombay, 1961 [16] Tate, J.T.: The arithmetic of elliptic curves, Inv. Math.23, pp. 179-206 (1974) · Zbl 0296.14018 · doi:10.1007/BF01389745 [17] Weil, A.: La Cyclotomie jadis et naguère, Seminaire Bourbaki no, 452, 1973/74 [18] Whittaker, E.T., Watson, G.N.: A course of modern analysis, Cambridge: Cambridge University Press, 1962 · Zbl 0105.26901 [19] Coates, J., Lichtenbaum, S.: Onl-adic zeta functions. Annals of Math.98, 498-550 (1973) · Zbl 0279.12005 · doi:10.2307/1970916 [20] Lang, S.: Cyclotomic Fields, Berlin-Heidelberg-New York: Springer Verlag 1978 · Zbl 0395.12005 [21] Katz, N.:p-adicL-functions via moduli of elliptic curves. Proc. 1974 AMS Arcata Summer Institute in Algebraic Geometry, PSPM 29, AMS, Providence 1975 · Zbl 0317.14009 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.