Almost-universal quadratic forms: An effective solution of a problem of Ramanujan

  title={Almost-universal quadratic forms: An effective solution of a problem of Ramanujan},
  author={Jacek Bochnak and Byeong-Kweon Oh},
  journal={Duke Mathematical Journal},
The object of this paper is to prove several results giving an effective method for deciding whether a positive definite integral quaternary quadratic form is almost universal, that is, whether it represents all large positive integers. In this way we obtain an effective and definitive solution to a problem first addressed and investigated by Ramanujan 90 years ago (cf. [11]). The following set Σ = {1, 2, 3, 5, 6, 7, 10, 14} 

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  • Contemporary Math., 272. Amer. Math. Soc.,
  • 2000