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The Goldbach exceptional set: an exponent 7/12 and conditional refinement
Let \(E(X)\) count the even integers between \(4\) and \(X\) that are not sums of two primes. We combine Pintz's explicit formula for the major arcs with the exponential-sum estimate of Maynard, Pandey, and Radziwiłł to prove \(E(X)\ll_\varepsilon X^{7/12+\varepsilon}\) whenever all Dirichlet \(L\)-
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