A proof of the Riemann hypothesis, by Xian-Jin Li.
I'm not qualified to judge the correctness of this, but glancing through it, I see that it at least looks like mathematics. Most purported proofs of the Riemann hypothesis set off the crackpot alarm bells in my head; this one doesn't. Li has also stated Li's criterion in 1997, which is one of the many statements that's equivalent to RH, although I don't think it's used in the putative proof, and wrote a PhD thesis titled The Riemann Hypothesis For Polynomials Orthogonal On The Unit Circle (1993), so this is at least coming from someone who's been thinking about the problem for a while and is part of the mathematical community.
Is it normal to have that much elementary background in number theory articles?
ReplyDeleteI am also not qualified to judge on this and of course one should be skeptical. But I do not quite understand cooper's comment. Where do you see too much elementary background in this paper?
ReplyDelete(Perhaps it is because the headings of single chapters are a bit misleading. Chapter 2 does not define Haar measure and Chapter 6 does not define L2-functions, as one might have believed from the subtitle.)
Well what do you think this means??
ReplyDeleteI mean, sure it gets us a better understanding of the distribution of prime numbers, but essentially it just says they behave more statistically like random coin flips. What does that give us- and, anyone know what Li's Criterion or other RH equivalents mean?
Li's Criterion in particular has been generalized to other analytic functions so seems very important...
Looks like there's a problem with the proof. Here's a post from Not Even Wrong.
ReplyDeletetk,
ReplyDeletePerhaps I shouldn't have said 'elementary'. I certainly didn't think the author was defining L2!
And I didn't say 'too much', only 'that much'; it's always good to fix notation and make sure everybody knows your conventions.