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It's not entirely fair to call the second point a major slip. I think that it is still sort of inaccurate, but not exactly for the reason I had said above; see
by gavagai691 5y ago
It's not entirely fair to call the second point a major slip. I think that it is still sort of inaccurate, but not exactly for the reason I had said above; see the thread following kevinventullo's comment below. In any case, my second point is sort of pedantic. I don't love the terminology used, but I wouldn't heap very much blame on the author.
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.
- civilized 5y agoIan 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. [1] https://www.ucl.ac.uk/~ucahpet/SubconvexityIntro.pdf https://www.ucl.ac.uk/~ucahpet/SubconvexityIntro.pdf
- gavagai691 5y agoBy 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..!