Re:Mathematicians clear hurdle in quest to decode primes
by civilized on Friday January 14, 2022 @11:12AM
(#29936233)
Ian Petrow defines the Subconvexity Problem as "Prove non-trivial upper bounds for L-functions on the critical line" [1]
Given that, it seems fair-ish to say that Nelson solved the Subconvexity Problem. You just have to understand that the problem is really a family of problems of increasing hardness (e.g. prove tighter and tighter bounds), and solutions more powerful than Nelson's may come later.
Re:Mathematicians clear hurdle in quest to decode primes
by gavagai691 on Friday January 14, 2022 @11:31AM
(#29936570)
By that definition, I agree, if you add the qualifier "Nelson solved the subconvexity problem for for automorphic L-functions."
I still think it's vague to talk about "the" subconvexity problem without specifying what variable you want the bound to be subconvex in, but, really, who am I to argue with Ian Petrow..!
The first one is a bit worse. I think if I had read this knowing nothing about convexity I would have gotten the wrong idea from the arbitrary choice of 1%. I understand the desire to simplify, but it is an art to simplify while keeping what you say technically correct. Quanta usually does an excellent job of this. I wouldn't say that the first point above is an egregious error by any means, but I think it is a slip.