## 02 July 2008

### Li's proof of Riemann?

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.

thecooper said...

Is it normal to have that much elementary background in number theory articles?

tk said...

I 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?
(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.)

Dran said...

Well what do you think this means??

I 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...

John said...

Looks like there's a problem with the proof. Here's a post from Not Even Wrong.

thecooper said...

tk,

Perhaps 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.