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, Tome 3 (1976) no. 4, pp. 623-663.
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     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},
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     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/}
}
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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, Tome 3 (1976) no. 4, pp. 623-663. http://www.numdam.org/item/ASNSP_1976_4_3_4_623_0/

[1] A. Baker, Linear forms in the logarithms of algebraic numbers, Mathematika, 13 (1966), pp. 204-216. | MR | Zbl

[2] A. Baker, Imaginary quadratic fields with class number two, Annals of Math., 94 (1971), pp. 139-152. | MR | Zbl

[3] B.J. Birch - N.M. Stephens, The parity of the rank of the Mordell-Weil group, Topology, 5 (1966), pp. 295-299. | MR | Zbl

[4] B.J. Birch - H.P.F. Swinnerton-Dyer, Notes on elliptic curves, J. reine angewandte Math., 218 (1965), pp. 79-108. | MR | Zbl

[5] M. Deuring, 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] D.M. Goldfeld, 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] D.M. Goldfeld, A simple proof of Siegel's theorem, Proc. Nat. Acad. Sciences U.S.A., 71 (1974), pp. 1055. | MR | Zbl

[8] D.M. Goldfeld - S. Chowla, On the twisting of Epstein zeta functions into Artin-Hecke L-series of Kummer fields, to appear.

[9] D.M. Goldfeld - A. Schinzel, On Siegel's zero, Annali Scuola Normale Superiore, Serie IV, 2 (1975), pp. 571-585. | Numdam | MR | Zbl

[10] E. Hecke, 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] E. Hecke, 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] E. Hecke, Vorlesung über die Theorie der algebraischen Zahlen, Leipzig (1923). | Zbl

[13] K. Heegner, Diophantische Analysis und Modulfunktionen, Math. Zeit., 56 (1952), pp. 227-253. | MR | Zbl

[14] K. Iseki, On the imaginary quadratic fields of class number one or two, Jap. J. Math., 21 (1951), pp. 145-162. | MR | Zbl

[15] A.F. Lavrik, Funktional equations of Dirichlet functions, Soviet Math. Dokl., 7 (1966), pp. 1471-1473. | Zbl

[16] L.J. Mordell, Diophantine Equations, Academic Press, London (1969). | MR | Zbl

[17] A.P. Ogg, On a convolution of L-series, Inventiones Math., 7 (1969), pp. 297-312. | MR | Zbl

[18] C.L. Siegel, Über die Classenzahl quadratischer Zahlkörper, Acta Arith., 1 (1935), pp. 83-86. | JFM | Zbl

[19] H.M. Stark, A complete determination of the complex quadratic fields with class number one, Mich. Math. J., 14 (1967), pp. 1-27. | MR | Zbl

[20] H.M. Stark, A transcendence theorem for class number problems, Annals of Math., 94 (1971), pp. 153-173. | MR | Zbl

[21] N.M. Stephens, 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] J. Tate, Algebraic cycles and poles of zeta-functions, Arithmetical Algebraic Geometry, New York (1965), pp. 93-110. | MR | Zbl

[23] A. Weil, Über die Bestimmung Dirichletscher Reihen durch Funktionalgleichungen, Math. Amm., 168 (1967), pp. 149-156. | MR | Zbl

[24] A. Wiman, Über rational Punkte auf Kurven y2 = x(x2- c2), Acta Math., 77 (1945), pp. 281-320. | MR | Zbl