Euler constants for a Fuchsian group of the first kind
We prove that the error term differs from (ψ(x)-x)/x by a well controlled function. We deduce very precise numerical results from the formula obtained.
Let χ be a primitive Dirichlet character of conductor q and denote by L(z,χ) the associated L-series. We provide an explicit upper bound for |L(1,χ)| when 3 divides q.