Ferrero, Bruce; Greenberg, Ralph On the behavior of \(p\)-adic \(L\)-functions at \(s=0\). (English) Zbl 0441.12003 Invent. Math. 50, 91-102 (1978). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 9 ReviewsCited in 53 Documents MSC: 11S40 Zeta functions and \(L\)-functions 11S80 Other analytic theory (analogues of beta and gamma functions, \(p\)-adic integration, etc.) 11R18 Cyclotomic extensions Keywords:Leopoldt-Kubota p-adic L-function; Dirichlet character; cyclotomic fields Citations:Zbl 0308.12003; Zbl 0406.12010 × Cite Format Result Cite Review PDF Full Text: DOI EuDML References: [1] Barsky: Fonctions Zetap-adiques d’une Classe de Rayon des Corps de Nombres Totalement-reels. Preprint · Zbl 0406.12008 [2] Brumer, A.: On the Units of Alebraic Number Fields. Mathematika14, 121-124 (1967) · Zbl 0171.01105 · doi:10.1112/S0025579300003703 [3] Cassou-Nogues, P.: Valeurs sur les Entiers des Fonctions Zeta des Corps de Nombres et des FonctionsL des Courbes Elliptiques. Thesis, Universite de Bordeaux (1978) · Zbl 0411.12008 [4] Coates, J., Lichtenbaum, S.: Onl-adic Zeta Functions. Ann. of Math.98, 498-550 (1973) · Zbl 0279.12005 · doi:10.2307/1970916 [5] Deligne, P., Ribet, K.: Values of AbelianL-functions at Negative Integers. In press (1978) [6] Diamond, J.: On the Values ofp-adicL-functions at Positive Integers. In press (1978) [7] Ferrero, B., Washington, L.: The Iwasawa Invariant? p Vanishes for Abelian Number Fields. Ann. of Math. In. press (1978) · Zbl 0443.12001 [8] Gross, B., Koblitz, N.: Gauss Sums and thep-adic ?-function. In press (1978) [9] Greenberg, R.: On a Certainl-adic Representation. Inventiones Math.21, 117-124 (1973) · Zbl 0268.12004 · doi:10.1007/BF01389691 [10] Greenberg, R.: Onp-adicL-functions and Cyclotomic Fields. Nagoya Math. Jour.56, 61-77 (1974) [11] Greenberg, R.: Onp-adicL-functions and Cyclotomic Fields II. Nagoya Math. Jour.67, 139-158 (1977) · Zbl 0373.12007 [12] Iwasawa, K.: Lectures onp-adicL-functions. Ann. Math. Studies74, Princeton University Press 1972 [13] Iwasawa, K.: On Z l -extensions of Algebraic Number Fields. Ann. of Math.98, 246-326 (1973) · Zbl 0285.12008 · doi:10.2307/1970784 [14] Kubota, T., Leopoldt, H.: Einep-adische Theorie der Zetawerte (Teil I). J. Reine Angew. Math.213, 328-339 (1964) · Zbl 0186.09103 [15] Morita, Y.: Ap-adic Analogue of the ?-function. J. Fac. Science Univ Tokyo 22, 255-266 (1975) · Zbl 0308.12003 [16] Whittaker, E.T., Watson, G.N.: A Course of Modern Analysis, 4th Edition. Cambridge University Press London 1927 · JFM 53.0180.04 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.