MathOverflow

I am studying a family of non‑homogeneous linear complex differential equations and encountered the following limit. I would like an explicit counterexample, if one exists.
For $w\in\mathbb{C}_+:=\{z\in\mathbb{C}:\Re(z)>0\}$ define$$\mu_\eta(w) = -1-(1-w)\int_1^{+\infty} u^{-1-w}\,\eta(u)\,du .$$(The integral converges absolutely because $\Re(w)>0$ and $\eta$ is bounded.)...

In computational complexity, $P \ne NP$ is a widely believed conjecture. Suppose that someone discovered a proof for it. He wants to publish a proof that he correctly proved the conjecture. I am aware that NP-complete problems have Zero-knowledge proofs...

Does anyone have any insight into why it is so hard to prove that P != NP conjecture? There seems to be so much evidence in its favor, and so many problems and techniques with which to attack it, that I don't get why it has remained unproven for so long...

It is a well-known state of affairs that, while there is a rich obstruction theory for Einstein metrics in dimension four (and, of course, in lower dimensions the uniformization theorem and Thurston's geometrization conjecture settle the issue entirely...