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A new explicit formula in the additive theory of primes with applications I. The explicit formula for the Goldbach and Generalized Twin Prime Problems

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arxiv 1804.05561 v1 pith:CIDWK6A6 submitted 2018-04-16 math.NT

Janos Pintz This is my paper · ORCID
classification math.NT
keywords explicitformulaapplicationsarcsgeneralizedgoldbachmajorprime
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A new explicit formula is proved for the contribution of the major arcs in the Goldbach and Generalized Twin Prime Problem, in which the level of the major arcs can be chosen very high. This will have many applications in the approximations of the mentioned problems.

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  1. The exceptional set of the Goldbach problem

    math.NT 2026-07 conditional novelty 5.0 of 10

    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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