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Nov 26, 2015 at 21:04 comment added TOM Mikhail: The paper is either correct or it is not, there can be no modulo. And you are indeed correct - this is not just a problem - it is a major problem in the field and so the standards should be higher. It is not the job of the referee to sit down and work on the details for weeks. No one has to do this work but the author or some person he could hire.
Aug 2, 2014 at 0:18 comment added zeb Better example: we can take $x$ very small, $m=1,n=10$, $p=1+x$, and $q = 2-\log(\log(1/x))/\log(1/x) + O(x)$.
Aug 1, 2014 at 23:23 comment added Mikhail No, they are positive constants independent of x. It is important that x is sufficiently small, for given value it can be not true. If minimums are equal, you can skip these exponentials and continue. But I just come across the discussion in this blog and reply. Not excellent writing paper is disadvantage but when famous problem is solved not just regular research is made, I think the most important thing is whether the proof is right modulo some corrections or not
Aug 1, 2014 at 23:06 comment added zeb The thing that makes me suspicious here is that $m,n,p,q$ seem to be functions of $x$, not constants. In this case I think the only thing one can really conclude is that the minimum of $m,n$ is close to the minimum of $p,q$. For instance, I don't see what rules out situations like $100^{-1} + 100^{-10} = 100^{-1.01} + 100^{-1.67335...}$.
Aug 1, 2014 at 22:40 review First posts
Aug 1, 2014 at 22:46
Aug 1, 2014 at 22:36 history answered Mikhail CC BY-SA 3.0