Proves asymptotic for the number of ternary Goldbach representations of large odd N with one prime bounded by U = N^{4/49} exp(log^{2/3+ε}N) unconditionally or log^{4+ε}N under GRH.
Davenport, On some infinite series involving arithmetical functions (II), Quart
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On the Goldbach problem with restricted primes
Proves asymptotic for the number of ternary Goldbach representations of large odd N with one prime bounded by U = N^{4/49} exp(log^{2/3+ε}N) unconditionally or log^{4+ε}N under GRH.