Non-asymptotic bounds for prime counting function for arithmetic progressions

46 Views Asked by At

Are there non-asymptotic bounds for prime counting function $\pi_{a,b}(x)$ for arithmetic progressions $a+kb$, where $a$ and $b$ are coprime?

I found asymptotic bounds for $\pi_{a,b}(x)$ and non-asymptotic for usual prime counting function $\pi(x)$, but wasn't able to find any non-asymptotic bounds for $\pi_{a,b}(x)$ .