• Corpus ID: 59408183

The class number of quadratic fields and the conjectures of Birch and Swinnerton-Dyer

@article{Goldfeld1976TheCN,
  title={The class number of quadratic fields and the conjectures of Birch and Swinnerton-Dyer},
  author={Dorian Goldfeld},
  journal={Annali Della Scuola Normale Superiore Di Pisa-classe Di Scienze},
  year={1976},
  volume={3},
  pages={623-663}
}
  • D. Goldfeld
  • Published 1976
  • Mathematics
  • Annali Della Scuola Normale Superiore Di Pisa-classe Di Scienze
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The conjectures of Birch and Swinnerton-Dyer and the class numbers of quadratic fields
© Société mathématique de France, 1977, tous droits réservés. L’accès aux archives de la collection « Astérisque » (http://smf4.emath.fr/ Publications/Asterisque/) implique l’accord avec les
Class numbers of imaginary quadratic fields
  • M. Watkins
  • Computer Science, Mathematics
    Math. Comput.
  • 2004
TLDR
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We aim to re-prove a theorem conjectured by Gauss, namely there are exactly 9 imaginary quadratic fields Q( √ −q) with class number 1: specifically the list is q ∈ {3, 4, 7, 8, 11, 19, 43, 67, 163}.
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a result first proved by Heilbronn [H] in 1934. The Disquisitiones also contains tables of binary quadratic forms with small class numbers (actually tables of imaginary quadratic fields of small
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L’accès aux archives de la revue « Annali della Scuola Normale Superiore di Pisa, Classe di Scienze » (http://www.sns.it/it/edizioni/riviste/annaliscienze/) implique l’accord avec les conditions
A Simple Proof of Siegel's Theorem.
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    Proceedings of the National Academy of Sciences of the United States of America
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A brief and simple proof of Siegel's celebrated theorem that h(d) >> d(1/2-[unk]), as d --> infinity, is given. Here h(d) denotes the class number of the quadratic field Q([unk]-d). Simple proofs
ON FUNCTIONAL EQUATIONS OF DIRICHLET FUNCTIONS
The paper adduces a theorem of a general form on functional equations of the Dirichlet functions, as well as certain of its corollaries.
Über die Bestimmung Dirichletscher Reihen durch Funktionalgleichungen
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A Transcendence Theorem for Class-Number Problems (II)
Imaginary quadratic fields with class number 2
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