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

Abstract:

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 Brüdern 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-prim...

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D. R. Heath-Brown More by this author
D. I. Tolev More by this author
Publication date:
2003
URN:
uuid:9dec2755-0d08-48ee-bf68-f6c15dfb3832
Local pid:
oai:eprints.maths.ox.ac.uk:141

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