@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},
publisher = {Scuola normale superiore},
volume = {Ser. 4, 3},
number = {4},
year = {1976},
pages = {623-663},
zbl = {0345.12007},
mrnumber = {450233},
language = {en},
url = {http://www.numdam.org/item/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, Série 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 258756 | Zbl 0161.05201
[2] , Imaginary quadratic fields with class number two, Annals of Math., 94 (1971), pp. 139-152. | MR 299583 | Zbl 0219.12008
[3] - , The parity of the rank of the Mordell-Weil group, Topology, 5 (1966), pp. 295-299. | MR 201379 | Zbl 0146.42401
[4] - , Notes on elliptic curves, J. reine angewandte Math., 218 (1965), pp. 79-108. | MR 179168 | Zbl 0147.02506
[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 404212 | Zbl 0327.10042
[7] , A simple proof of Siegel's theorem, Proc. Nat. Acad. Sciences U.S.A., 71 (1974), pp. 1055. | MR 344222 | Zbl 0287.12019
[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 404213 | Zbl 0327.10041
[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 47.0152.01
[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 47.0144.01
[12] , Vorlesung über die Theorie der algebraischen Zahlen, Leipzig (1923). | Zbl 0057.27301
[13] , Diophantische Analysis und Modulfunktionen, Math. Zeit., 56 (1952), pp. 227-253. | MR 53135 | Zbl 0049.16202
[14] , On the imaginary quadratic fields of class number one or two, Jap. J. Math., 21 (1951), pp. 145-162. | MR 51261 | Zbl 0054.02301
[15] , Funktional equations of Dirichlet functions, Soviet Math. Dokl., 7 (1966), pp. 1471-1473. | Zbl 0209.34801
[16] , Diophantine Equations, Academic Press, London (1969). | MR 249355 | Zbl 0188.34503
[17] , On a convolution of L-series, Inventiones Math., 7 (1969), pp. 297-312. | MR 246819 | Zbl 0205.50902
[18] , Über die Classenzahl quadratischer Zahlkörper, Acta Arith., 1 (1935), pp. 83-86. | JFM 61.0170.02 | Zbl 0011.00903
[19] , A complete determination of the complex quadratic fields with class number one, Mich. Math. J., 14 (1967), pp. 1-27. | MR 222050 | Zbl 0148.27802
[20] , A transcendence theorem for class number problems, Annals of Math., 94 (1971), pp. 153-173. | MR 297715 | Zbl 0229.12010
[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 229651 | Zbl 0221.10023
[22] , Algebraic cycles and poles of zeta-functions, Arithmetical Algebraic Geometry, New York (1965), pp. 93-110. | MR 225778 | Zbl 0213.22804
[23] , Über die Bestimmung Dirichletscher Reihen durch Funktionalgleichungen, Math. Amm., 168 (1967), pp. 149-156. | MR 207658 | Zbl 0158.08601
[24] , Über rational Punkte auf Kurven y2 = x(x2- c2), Acta Math., 77 (1945), pp. 281-320. | MR 14721 | Zbl 0061.07110
