Lagrange's four squares theorem with one prime and threealmost--prime variables

@article{HeathBrown2003LagrangesFS,
  title={Lagrange's four squares theorem with one prime and threealmost--prime variables},
  author={D. R. Heath-Brown and D. Tolev},
  journal={Crelle's Journal},
  year={2003},
  volume={2003},
  pages={159-224}
}
It is conjectured that every sufficiently large integer $N\equiv 4\pmod{24}$ should be a sum of the squares of 4 primes. The best approximation to this in the literature is the result of Brudern and Fouvry [J. Reine Angew. Math., 454 (1994), 59--96] who showed that every sufficiently large integer $N\equiv 4\pmod{24}$ is a sum of the squares of 4 almost-primes, each of which has at most 34 prime factors. The present paper proves such a result with the square of one prime and 3 almost-primes… Expand
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