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

作者：Meng Xianmeng^*

来源：Monatshefte fur Mathematik, 2007, 151(4): 319-332.

DOI：10.1007/s00605-007-0456-6

• the Hardy-Littlewood method
• sieve methods
• additive problems

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 6 not equal 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 n satisfying n not equivalent to 1(mod 6), the equation p(1) + p(2) + p(3) = 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.

• 出版日期2007-8
• 单位山东财经大学