Lindelöf hypothesis

Today I stumbled across a news article ( link ) written about someone (actually, Athanassios Fokas – a known mathematician) having announced progress on the Lindelöf hypothesis ( wikipedia ). The Lindelöf hypothesis is related to the Riemannian hypothesis and actually also follows from it – progress on the Lindelöf hypothesis would also mean progress on the Riemannian hypothesis.

As I expected, the corresponding arXiv article ( arXiv:1708.06607 ) has already undergone several iterations (even claiming in the second one a proof of the Lindelöf hypothesis) and does by now not claim major progress on the Lindelöf problem, but only a novel approach which might become useful. See also the short discussion at MathOverflow: link.

Why am I writing about this here? There are many “proofs” of, e.g., the Riemannian hypothesis posted regularly and there is no need in general to talk about them. In this case, I enjoyed a bit reading the above cited news article and I did not know about the Lindelöf hypothesis – hence I wanted to share this with you.