Is there someone here who follows Riemann Hypothesis research closely enough to comment on whether there is any there here?[1] The Riemann Hypothesis is a sufficiently complicated and famous problem that I think it must be easy for a wishful thinker to suppose he has found a solution when he actually hasn't.<p>[1] This is a reference to a famous quotation from Gertrude Stein's autobiography, "anyway what was the use of my having come from Oakland it was not natural to have come from there yes write about it if I like or anything if I like but not there, there is no there there."<p><a href="https://en.wikipedia.org/wiki/Gertrude_Stein#.22There_is_no_there_there.22" rel="nofollow">https://en.wikipedia.org/wiki/Gertrude_Stein#.22There_is_no_...</a>
On page 4, it says "Now by Robin criterion d(n)<0 for n large enough, yielding lim sup (n->infinity) (d(n)) <= 0". If I understand the criterion from page 1 right, assuming RH is false only implies that d(n) <= 0 for some n > 7! -- not for all n sufficiently large, so the limit superior is not constrained as claimed. In fact, on page 2, the paper claims "Thus, if m is bounded and n->infinity, we see that d(n)->infinity", which, if the falsity of RH did imply lim sup (n->infinity) (d(n)) <= 0, would make for an even shorter and simpler proof.<p>Disclaimer: I've only got an undergrad in math and don't know much about the specifics of the cited papers, so I might be missing something.
There are dozens of papers attempting to prove the Riemann Hypothesis. Here is a list [1]. A joke from the author of the list: "It's easier to prove the RH than to get someone to read your proof".<p>[1] <a href="http://empslocal.ex.ac.uk/people/staff/mrwatkin//zeta/RHproofs.htm" rel="nofollow">http://empslocal.ex.ac.uk/people/staff/mrwatkin//zeta/RHproo...</a>
Coming from a PhD in math I can give this good trick for assessing grand mathematical claims:<p>Google the authors.<p>Maybe unfair to intelligent amateurs, but based on my decade of experience you find out from this whether to take something seriously.<p>Might need some adjustment of Google terms for hard-to-google names, just use common sense.
The description on researchgate says "work in progresswork in progresswork in progresswork in progresswork in progresswork in progresswork in progresswork in progresswork in progress". It seems unlikely that the author would write that if they really believed this was a complete work. It's just not worth posting purported proofs of the Riemann Hypothesis. There are dozens of them. Until someone serious comes forward and says, "we think this is a proof", it's not.
I'm just going to say "no way". No way that a 4-page document is the proof, and no way it's on any site other than a university or Arxiv.
At the end of Lemma 2, "[9, Th. 8, (39)]" seems to be referring to corollary 1 of Theorem 8 on page 70 of [1], equation (3.30). Maybe "(39)" is meant to be "(30)".<p>Their argument for Theorem 1 seems not-crazy, and quite accessible.<p>[1] <a href="https://projecteuclid.org/download/pdf_1/euclid.ijm/1255631807" rel="nofollow">https://projecteuclid.org/download/pdf_1/euclid.ijm/12556318...</a>
The paper uses results from "Grandes valeurs de la fonction somme des diviseurs et hypothèse de Riemann" by Robin, which is not available online, as far as I can tell.