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This is a reference request.

I know that Hardy and Littlewood gave a proof of the ternary Goldbach for sufficiently large odd integers under the assumption of GRH.

Is there a modern account of this proof?

Their paper is using the pre-Vinogradov version of the circle method which is rather hard to follow.

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    $\begingroup$ Here's a version of that proof (see pages 18-22): math.stanford.edu/~ksound/Notes.pdf By the way, the Hardy--Littlewood argument is better than what came later --- they put in natural smooth weights, which Vinogradov removed with sharp cut-offs, and which later ``modern" authors reintroduced! Such is progress. $\endgroup$
    – Lucia
    Commented Mar 6, 2017 at 1:50
  • $\begingroup$ Thanks for the link! PS.I think it is also important to be able to solve difficult for sufficiently small integers, especially in analytic number theory. $\endgroup$
    – Dr. Pi
    Commented Mar 6, 2017 at 23:25
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    $\begingroup$ Sure, but my comment is with reference to your statement that Hardy-Littlewood are using a "pre-Vinogradov version ... which is rather hard to follow." Vinogradov's innovation was for the minor arcs, the rest of Hardy-Littlewood is pretty "modern." For example, they note that only no zeros to the right of $3/4$ is needed, and this is not immediate! $\endgroup$
    – Lucia
    Commented Mar 7, 2017 at 3:38

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