The Ternary Goldbach Problem

@article{HeathBrown1985TheTG,
  title={The Ternary Goldbach Problem},
  author={Roger Heath-Brown},
  journal={Revista Matematica Iberoamericana},
  year={1985},
  volume={1},
  pages={45-59}
}
The object of this paper is to present new proofs of the classical ternary theorems of additive prime number theory. Of these the best known is Vinogradov's result on the representation of odd numbers as the sums of three primes; other results will be discussed later. Earlier treatments of these problems used the Hardy-Littlewood circle method, and are highly analytical. In contrast, the method we use here is a (technically) elementary deduction from the Siegel-Walfisz Prime Number Theory. It… 

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References

SHOWING 1-6 OF 6 REFERENCES
History of the Theory of Numbers
THE third and concluding volume of Prof. Dickson's great work deals first with the arithmetical. theory of binary quadratic forms. A long chapter on the class-number is contributed by Mr. G. H.
Numerical verification of ternary Goldbach , To appear
  • 1966
Liu and T
  • Wang, On the Vinogradov bound in the three primes Goldbach conjecture, Acta Arith. 105 (2002), no. 2, 133–175, ISSN 0065-1036, http://dx.doi.org/10.4064/aa105-2-3. MR 1932763
  • 1147
La conjecture de Goldbach ternaire, Preprint
  • La conjecture de Goldbach ternaire, Preprint
Numerical verification of ternary Goldbach
  • Numerical verification of ternary Goldbach