3 ms·

If anyone is going to solve the RH, it would be after numerous failed attempts.

gus_massa 4y ago
Most people wait until they are almost sure that the proof is correct before publishing it, with a few informal reviews of coworkers. It's strange that he posted so many versions. Is this [v19] version the final correct one or he is going to post a fix in a few weeks?
- Quant10 4y ago
  I wouldn't know. But from the author's arXiv statement [1] that ..though all of my previous (dis)proofs were flawed, i think the flaws pointed me towards the right direction..." it seems they are quite confident in the current version. [1] https://arxiv.org/abs/2006.12546 https://arxiv.org/abs/2006.12546
  - gus_massa 4y ago
    I've read that, but looking at the previous history I'd wait a month before reading it in case the author finds yet another error. (Unless you are a specialist in the subject.)
    - Quant10 4y ago
      I'm a physics major, unfortunately. But i have taken some basic courses in number theory & analysis. As far as i can tell, the argument looks interesting (can't find any serious fault in it). However, i can't say anything conclusive. Maybe someone else will.
mjreacher 4y ago
There have been lots of attempts by people trying to solve the RH and quite a few of them use the exact same kind of circular logic that is demonstrated in the paper.
- Quant10 4y ago
  Can you share the links to those papers which you claim to be logically "similar" to this one? And, if you want to be critical, just point out some part(s) of the proof you believe to be flawed and justify why you think so. That's how mathematics works.
  - mjreacher 4y ago
    https://www.google.com/search?q=riemann+hypothesis+site%3Avixra.org https://www.google.com/search?q=riemann+hypothesis+site%3Avi... If you've studied real analysis some of the integrals don't converge the way the paper claims they do (I think Lubos makes similar comments on the page you linked in one of the sister comments).
    - deleted 4y ago
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    - Quant10 4y ago
      May you explicitly and clearly point out the integrals you are referring to ? Anyway, by quoting Lubos Motl's blog post of 2018/19, i'm lead to guess you are talking about the integrals on the extreme right-hand side of (13) and (14). Indeed, the author clearly and rigorously showed that those integrals are absolutely convergent and real-analytic for sigma > Theta, such that f(sigma) and g(sigma) both have real- analytic continuations there. In the 2018 version that was reviewed by Lubos, the author had an equation of the form A(s) = B(s) for Re(s)>1, where A(s) is some improper integral and B(s) is some function that is analytic in some (larger) half-plane. From this, one can only deduce that A(s) has an analytic continuation to the larger plane, but one cannot deduce (as the author did in that 2018 version) that A(s) converges there. For example, let A(s) be the integral of x^{-s} w.r.t. x on [1, infty). Then B(s) = (s-1)^{-1} for Re(s) > 1. Notice that B(s) hence A(s) has a meromorphic continuation to the entire complex plane with a (simple) pole only at s=1. However, one cannot deduce from this that A(s) converges for some s with Re(s) < 1. The mistake in the author's previous version is analogous to saying that A(s) converges for Re(s) < 1. However, to his credit, he seems to have been working hard to eliminate these kinds of mistakes. I guess that's what he means on his arXiv page when he said, "though all of my previous proposed (dis)proofs were flawed, i think the flaws pointed me towards the right direction". Credit where it's due.

Most people wait until they are almost sure that the proof is correct before publishing it, with a few informal reviews of coworkers. It's strange that he posted so many versions. Is this [v19] version the final correct one or he is going to post a fix in a few weeks?

Quant10 4y ago
I wouldn't know. But from the author's arXiv statement [1] that ..though all of my previous (dis)proofs were flawed, i think the flaws pointed me towards the right direction..." it seems they are quite confident in the current version. [1] https://arxiv.org/abs/2006.12546 https://arxiv.org/abs/2006.12546
- gus_massa 4y ago
  I've read that, but looking at the previous history I'd wait a month before reading it in case the author finds yet another error. (Unless you are a specialist in the subject.)
  - Quant10 4y ago
    I'm a physics major, unfortunately. But i have taken some basic courses in number theory & analysis. As far as i can tell, the argument looks interesting (can't find any serious fault in it). However, i can't say anything conclusive. Maybe someone else will.

mjreacher 4y ago

There have been lots of attempts by people trying to solve the RH and quite a few of them use the exact same kind of circular logic that is demonstrated in the paper.

Quant10 4y ago
Can you share the links to those papers which you claim to be logically "similar" to this one? And, if you want to be critical, just point out some part(s) of the proof you believe to be flawed and justify why you think so. That's how mathematics works.
- mjreacher 4y ago
  https://www.google.com/search?q=riemann+hypothesis+site%3Avixra.org https://www.google.com/search?q=riemann+hypothesis+site%3Avi... If you've studied real analysis some of the integrals don't converge the way the paper claims they do (I think Lubos makes similar comments on the page you linked in one of the sister comments).
  - deleted 4y ago
    [deleted]
  - deleted 4y ago
    [deleted]
  - Quant10 4y ago
    May you explicitly and clearly point out the integrals you are referring to ? Anyway, by quoting Lubos Motl's blog post of 2018/19, i'm lead to guess you are talking about the integrals on the extreme right-hand side of (13) and (14). Indeed, the author clearly and rigorously showed that those integrals are absolutely convergent and real-analytic for sigma > Theta, such that f(sigma) and g(sigma) both have real- analytic continuations there. In the 2018 version that was reviewed by Lubos, the author had an equation of the form A(s) = B(s) for Re(s)>1, where A(s) is some improper integral and B(s) is some function that is analytic in some (larger) half-plane. From this, one can only deduce that A(s) has an analytic continuation to the larger plane, but one cannot deduce (as the author did in that 2018 version) that A(s) converges there. For example, let A(s) be the integral of x^{-s} w.r.t. x on [1, infty). Then B(s) = (s-1)^{-1} for Re(s) > 1. Notice that B(s) hence A(s) has a meromorphic continuation to the entire complex plane with a (simple) pole only at s=1. However, one cannot deduce from this that A(s) converges for some s with Re(s) < 1. The mistake in the author's previous version is analogous to saying that A(s) converges for Re(s) < 1. However, to his credit, he seems to have been working hard to eliminate these kinds of mistakes. I guess that's what he means on his arXiv page when he said, "though all of my previous proposed (dis)proofs were flawed, i think the flaws pointed me towards the right direction". Credit where it's due.