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Old 2022-10-10, 14:46   #1
Tatenda
 
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Default [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 non-number 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.
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File Type: pdf Disproof of the Riemann hypothesis.pdf (246.5 KB, 133 views)
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Old 2022-10-10, 17:49   #2
pinhodecarlos
 
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You made my day, thank you. Why not submit to a math journal for example.
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Old 2022-10-10, 17:58   #3
Tatenda
 
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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.
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Old 2022-10-11, 01:09   #4
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Quote:
Originally Posted by Tatenda View Post
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 non-number 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.
Folk scientist????
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Old 2022-10-11, 01:58   #5
LaurV
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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?
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Old 2022-10-11, 06:21   #6
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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.
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Old 2022-10-13, 12:34   #7
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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:
This manuscript is four pages long, and will probably be the final paper in my study of the Riemann Hypothesis.
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Old 2022-10-13, 21:37   #8
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Perhaps in a couple of years they will have proved the supremum is at least 5/4
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Old 2022-10-14, 01:21   #9
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As a non-number 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:
Originally Posted by LaurV View Post
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?
No, that's not what it means for the supremum to equal 1. The author does at least seem to understand the basics.

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Originally Posted by Tatenda View Post
Clueless hater
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.
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Old 2022-10-14, 02:27   #10
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Quote:
Originally Posted by charybdis View Post
No, that's not what it means for the supremum to equal 1. The author does at least seem to understand the basics.
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 2022-10-14 at 02:30
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Old 2022-10-14, 02:33   #11
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Quote:
Originally Posted by LaurV View Post
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.
I don't see any statistics or probabilities in the OP's claimed proof. The claim is that if the supremum is less than 1, then a certain function has a pole in a region where an analytic continuation is known to exist, giving a contradiction. The supremum enters the proof through its well-known appearance in the error term for the Prime Number Theorem.
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