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.