Gauss’ class number problem for imaginary quadratic fields

@article{Goldfeld1985GaussCN,
  title={Gauss’ class number problem for imaginary quadratic fields},
  author={Dorian Goldfeld},
  journal={Bulletin of the American Mathematical Society},
  year={1985},
  volume={13},
  pages={23-37}
}
  • D. Goldfeld
  • Published 1 July 1985
  • Mathematics
  • Bulletin of the American Mathematical Society
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 class number with even discriminant which is a much easier problem to deal with) and Gauss conjectured that his tables were complete. In modern parlance, we can rewrite Gauss’ tables (we are including both even and odd discriminants) in the following form. 

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