Past exam of the mathematics course of the University of Cambridge / 2019 / iii / Paper 150 / 4 / d

Let ${\chi }_1$ be the real character associated with the exceptional zero $\beta$. The prime number theorem in an arithmetic progression with an exceptional zero gives, uniformly for $x\ge 2$ and $(a,q)=1$,If no exceptional zero exists, the middle term is omitted. The constant $c>0$ is absolute.