@article{ASNSP_1976_4_3_4_623_0, author = {Goldfeld, Dorian M.}, title = {The class number of quadratic fields and the conjectures of {Birch} and {Swinnerton-Dyer}}, journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze}, pages = {623--663}, publisher = {Scuola normale superiore}, volume = {Ser. 4, 3}, number = {4}, year = {1976}, mrnumber = {450233}, zbl = {0345.12007}, language = {en}, url = {http://www.numdam.org/item/ASNSP_1976_4_3_4_623_0/} }
TY - JOUR AU - Goldfeld, Dorian M. TI - The class number of quadratic fields and the conjectures of Birch and Swinnerton-Dyer JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 1976 SP - 623 EP - 663 VL - 3 IS - 4 PB - Scuola normale superiore UR - http://www.numdam.org/item/ASNSP_1976_4_3_4_623_0/ LA - en ID - ASNSP_1976_4_3_4_623_0 ER -
%0 Journal Article %A Goldfeld, Dorian M. %T The class number of quadratic fields and the conjectures of Birch and Swinnerton-Dyer %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 1976 %P 623-663 %V 3 %N 4 %I Scuola normale superiore %U http://www.numdam.org/item/ASNSP_1976_4_3_4_623_0/ %G en %F ASNSP_1976_4_3_4_623_0
Goldfeld, Dorian M. The class number of quadratic fields and the conjectures of Birch and Swinnerton-Dyer. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 3 (1976) no. 4, pp. 623-663. http://www.numdam.org/item/ASNSP_1976_4_3_4_623_0/
[1] Linear forms in the logarithms of algebraic numbers, Mathematika, 13 (1966), pp. 204-216. | MR | Zbl
,[2] Imaginary quadratic fields with class number two, Annals of Math., 94 (1971), pp. 139-152. | MR | Zbl
,[3] The parity of the rank of the Mordell-Weil group, Topology, 5 (1966), pp. 295-299. | MR | Zbl
- ,[4] J. reine angewandte Math., 218 (1965), pp. 79-108. | MR | Zbl
- , Notes on elliptic curves,[5] Die Zetafunktion einer algebraischer Kurve von Geschlechte Eins, I, II, III, IV, Nachr. Akad. Wiss. Göttingen (1953), pp. 85-94; (1954), pp. 13-42; (1956), pp. 37-76; (1957), pp. 55-80.
,[6] An asymptotic formula relating the Siegel zero and the class number of quadratic fields, Annali Scuola Normale Superiore, Serie IV, 2 (1975), pp. 611-615. | Numdam | MR | Zbl
,[7] A simple proof of Siegel's theorem, Proc. Nat. Acad. Sciences U.S.A., 71 (1974), pp. 1055. | MR | Zbl
,[8] On the twisting of Epstein zeta functions into Artin-Hecke L-series of Kummer fields, to appear.
- ,[9] On Siegel's zero, Annali Scuola Normale Superiore, Serie IV, 2 (1975), pp. 571-585. | Numdam | MR | Zbl
- ,[10] Eine Neue Art von Zetafunktionen und ihre Beziehugen zur Verteilung der Primzahlen (II), Math. Zeit., 6 (1920), pp. 11-56 (Mathematische Werke, pp. 249-289). | JFM
,[11] Über die Kroneckersche Grenzformel für reelle quadratische Körper und die Klassenzahl relativ-Abelscher Körper, Verhandlung Natur. Gesellschaft Basel, 28 (1917), pp. 363-372 (Mathematische Werke, pp. 208-214). | JFM
,[12] Vorlesung über die Theorie der algebraischen Zahlen, Leipzig (1923). | Zbl
,[13] Diophantische Analysis und Modulfunktionen, Math. Zeit., 56 (1952), pp. 227-253. | MR | Zbl
,[14] On the imaginary quadratic fields of class number one or two, Jap. J. Math., 21 (1951), pp. 145-162. | MR | Zbl
,[15] Funktional equations of Dirichlet functions, Soviet Math. Dokl., 7 (1966), pp. 1471-1473. | Zbl
,[16] Diophantine Equations, Academic Press, London (1969). | MR | Zbl
,[17] On a convolution of L-series, Inventiones Math., 7 (1969), pp. 297-312. | MR | Zbl
,[18] Über die Classenzahl quadratischer Zahlkörper, Acta Arith., 1 (1935), pp. 83-86. | JFM | Zbl
,[19] A complete determination of the complex quadratic fields with class number one, Mich. Math. J., 14 (1967), pp. 1-27. | MR | Zbl
,[20] A transcendence theorem for class number problems, Annals of Math., 94 (1971), pp. 153-173. | MR | Zbl
,[21] The diophantine equation X3 + Y3 = DZ3 and the conjectures of Birch and Swinnerton-Dyer, J. reine angewandte Math., 231 (1968), pp. 121-162. | MR | Zbl
,[22] Algebraic cycles and poles of zeta-functions, Arithmetical Algebraic Geometry, New York (1965), pp. 93-110. | MR | Zbl
,[23] Über die Bestimmung Dirichletscher Reihen durch Funktionalgleichungen, Math. Amm., 168 (1967), pp. 149-156. | MR | Zbl
,[24] Über rational Punkte auf Kurven y2 = x(x2- c2), Acta Math., 77 (1945), pp. 281-320. | MR | Zbl
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