OK, I suppose I must provide a link to the new paper by Xian-Jin Li
with the simple title A proof of the Riemann hypothesis
. Like many around the blogosphere
, I have no intention of trying to decipher it, although the claimed proof, by a well known
number theorist, relies heavily on Fourier analysis and ideas from Connes NCG. In other words, it sounds highly promising. Despite the expertise of the author however, my hunch is that there's a flaw, because the claimed proof is mostly standard analysis. However, perhaps flaws in the proof will be easy to iron out using techniques from quantum information theory.Update: Terence Tao
believes there is an error in equation (6.9) on page 20. He comments that the Fourier transform really ought not to be this powerful. Given the standard analytical form of Fourier transform used in the claimed proof this would seem a reasonable statement, but perhaps in an $\omega$ categorical framework (where as usual we associate primes $p$ with categorical dimension) this could be modified to obtain a decomposition of the form (6.9).