"Well, a Riemann surface is a certain kind of Hausdorff space. You know what a
Hausdorff space is, don’t you? Its also compact, ok. I guess it is also a manifold.
Surely you know what a manifold is. Now let me tell you one non-trivial theorem,
the Riemann–Roch Theorem"
— Gian-Carlo Rota’s recollection of Lefschetz lecturing in the 1940’s
I come across the following integral in my work
$$\int_a^\infty \log\left(\frac{x^2-1}{x^2+1}\right)\textrm{d}x,$$
with $a>1$.
Does this integral converge ? what is its value depending on $a$ ?
