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A mean value theorem on the binary Goldbach problem and its application

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Abstract.

We study the binary Goldbach problem with one prime number in a given residue class, and obtain a mean value theorem. As an application, we prove that for almost all sufficiently large even integers n satisfying n ≢ 2(mod 6), the equation p 1 + p 2 = n is solvable in prime variables p 1, p 2 such that p 1 + 2 = P 3, and for every sufficiently large odd integer \({\bar n}\) satisfying \({\bar n}\) ≢ 1(mod 6), the equation p 1 + p 2 + p 3 = \({\bar n}\) is solvable in prime variables p 1, p 2, p 3 such that p 1 + 2 = P 2, p 2 + 2 = P 3. Here P k denotes any integer with no more than k prime factors, counted according to multiplicity.

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Authors and Affiliations

  1. Shandong Finance Institute, Jinan, P.R. China

    Xianmeng Meng

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  1. Xianmeng Meng
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Meng, X. A mean value theorem on the binary Goldbach problem and its application. Mh Math 151, 319–332 (2007). https://doi.org/10.1007/s00605-007-0456-6

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  • DOI: https://doi.org/10.1007/s00605-007-0456-6

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