20221010, 14:46  #1 
Oct 2022
D_{16} Posts 
[Not a] Disproof of the Riemann hypothesis
Dear number theorists,
Attached is a possible disproof of the Riemann hypothesis, which you can also download via this link: https://figshare.com/articles/prepri...ction/21261969 So far, I have shown the paper to several nonnumber theorists, and their general opinion is the approach is interesting and the argument seems to be sound. Your constructive comments are most welcome. Sincerely, Tatenda. 
20221010, 17:49  #2 
"Carlos Pinho"
Oct 2011
Milton Keynes, UK
2×3^{3}×5×19 Posts 
You made my day, thank you. Why not submit to a math journal for example.

20221010, 17:58  #3 
Oct 2022
13_{10} Posts 
Thanks for your comment. I have indeed submitted the paper to some journal. However, it would still be good to get some constructive feedback from here.

20221011, 01:09  #4  
"特朗普trump"
Feb 2019
朱晓丹没人草
10000100_{2} Posts 
Quote:


20221011, 01:58  #5 
Romulan Interpreter
"name field"
Jun 2011
Thailand
19×541 Posts 
So, let me understand this, you show that all the children are in the room (i.e. Re(z)<1, which by the way is known for about a hundred years or so), and then, from this, and without looking in the room, you magically deduce that not all of them are on the top of the cupboard (Re(z)=1/2), they didn't fit well there, and there are some of them who fell down and broke their legs?

20221011, 06:21  #6 
Oct 2022
13 Posts 
I would say the key idea of the proof is Theorem 1, which has some resemblence to Selberg's inequality, upon which his elementary proof of the PNT was based.

20221013, 12:34  #7  
Feb 2017
Nowhere
2×3×17×61 Posts 
This arXiv submission by the same author on the same subject, originally submitted in 2020 and revised 19 times in the intervening two years, purports to prove that the supremum of the real parts of zeroes is at least 3/4. The author's comments begin,
Quote:


20221013, 21:37  #8 
Dec 2021
2×3×7 Posts 
Perhaps in a couple of years they will have proved the supremum is at least 5/4

20221014, 01:21  #9  
Apr 2020
39D_{16} Posts 
As a nonnumber theorist who studied number theory to masters level, I don't see anything that immediately leaps out as total nonsense like with a lot of false proofs that get posted. Nevertheless, on balance of probabilities, I highly doubt that the proof is correct, and the constant revisions to the previous arXiv paper are not a good sign in that regard. I'll leave it to the referees to go through the paper properly; that's not my job, and while the theory is all stuff I've seen before, it's not exactly at the forefront of my mind.
Quote:
Ah yes, a very professional response. Needless to say, the supremum cannot be greater than 1. While I'm not absolutely sure, I assume that the poster knows that and is making a joke. 

20221014, 02:27  #10 
Romulan Interpreter
"name field"
Jun 2011
Thailand
10279_{10} Posts 
We know what supremum means. But taking some smaller and smaller neighborhood around 1, we don't see any points inside of that neighborhood. So, our clueless conclusion is that except for the part that "all roots are smaller than 1", the rest is statistics and probabilities. Which does not constitute a proof. Now, I don't lean in any direction with my beliefs, about this RH. Maybe one reason why is so hard to prove, and why nobody proved it until now, is the fact that it is false (!?). So, the author may have something here. But the way he goes seems fishy, albeit I am not qualified enough and clever enough to pinpoint an error.
Last fiddled with by LaurV on 20221014 at 02:30 
20221014, 02:33  #11  
Apr 2020
1635_{8} Posts 
Quote:


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