The number of Goldbach representations of an integer

Details The number of Goldbach representations of an integer The number of Goldbach representations of an integer

2010-11-14

arxiv.org/abs/1011.3198v1

Mathematics

Number Theory

Scientific paper

We prove the following result: Let $N \geq 2$ and assume the Riemann
Hypothesis (RH) holds. Then \[ \sum_{n=1}^{N} R(n) =\frac{N^{2}}{2} -2
\sum_{\rho} \frac{N^{\rho + 1}}{\rho (\rho + 1)} + O(N \log^{3}N), \] where
$\rho=1/2+i\gamma$ runs over the non-trivial zeros of the Riemann zeta function
$\zeta(s)$.

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