Hello,

Can anyone help me with the following implication of the GRH which is fundamental while proving the Odd Goldbach's Conjecture?

$$\psi(x,\chi):=\sum_{n\leq x}\Lambda(n)\chi(n)=O(x^{1/2}\log^2 x)$$ where $\chi$ is a non-trivial Dirichlet character.

Also tell me the difference in proof while considering the trivial Dirichlet Character, $\chi$.

Thank You.

sufficiently largeodd integer can be written as the sum of three primes; concluding this foreveryodd integer greater than 6 requires GRH (so far). – Greg Martin Oct 20 '12 at 3:26