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A new explicit formula in the additive theory of primes with applications II. The exceptional set in Goldbach's problem
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Improving earlier estimates of several authors we show that the number E(X) of Goldbach exceptional even integers (that is, even integers which cannot be written as the sum of two primesw) below X satisfies tho bound E(X) < X^0.72 for sufficiently large X. In the proof crucial role is played by the explicit formula for the contribution of the major arcs proved in Part I of this series (arXiv:1804.05561). In this new version some misprints are corrected and an explanatory sentence is added to the common proof of theorems C and D.
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The exceptional set of the Goldbach problem
A mostly expository paper on the exceptional set of the binary Goldbach problem, appending a smoothed fully explicit major-arc formula and a conditional theorem that a sparse Goldbach-type bound excludes Siegel zeros.
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