Mathematician-M.D. claims to have solved the 110-year-old Lindelöf hypothesis
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Mathematician-M.D. claims to have solved the 110-year-old Lindelöf hypothesis
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Re: Mathematician-M.D. claims to have solved the 110-year-old Lindelöf hypothesis
#2Can someone eli5 the lindelof hypothesis?
Re: Mathematician-M.D. claims to have solved the 110-year-old Lindelöf hypothesis
#3What exactly is the application for cyber security? How does this affect cryptography?
Re: Mathematician-M.D. claims to have solved the 110-year-old Lindelöf hypothesis
#4What exactly is the application for cyber security? How does this affect cryptography?
Nothing because it doesn’t show a method about the distribution of prime numbers but it says that given the Riemann hypothesis is true then the leinhoff problem is true .
Re: Mathematician-M.D. claims to have solved the 110-year-old Lindelöf hypothesis
#5What exactly is the application for cyber security? How does this affect cryptography?
I think it's because any information we gain about the Riemann Hypothesis (Lindelöf hypothesis is implied by RH) gives us information about the distribution of prime numbers. Any time you gain information about the distribution of prime numbers you immediately gain information that can be applied to any form of cryptography that makes use of prime numbers. You could use this information either to break existing forms of cryptography faster, or apply it to building newer and stronger cryptography.
Re: Mathematician-M.D. claims to have solved the 110-year-old Lindelöf hypothesis
#6What exactly is the application for cyber security? How does this affect cryptography?
I think it's because any information we gain about the Riemann Hypothesis (Lindelöf hypothesis is implied by RH) gives us information about the distribution of prime numbers. Any time you gain information about the distribution of prime numbers you immediately gain information that can be applied to any form of cryptography that makes use of prime numbers. You could use this information either to break existing forms…
So, people hire you to break into their places... to make sure no one can break into their places?
Re: Mathematician-M.D. claims to have solved the 110-year-old Lindelöf hypothesis
#7Can someone eli5 the lindelof hypothesis?
Not eli5, but a comparison to the Riemann Hypothesis (RH).
RH says the Riemann-zeta function has no zeros along the line (1/2) + iy in the complex plane.
The Lindelof hypothesis says that the number of zeros between (1/2) + iy and (1/2) + i(y+1) is much smaller (little-o) than log(y) as y grows.
So it can be thought of as a weaker version of RH, but still very very difficult. The fact that Lindelof has been an open problem for over a hundred years (and is an non-trivial weakening of RH) speaks to how difficult RH is as well.
Like RH, Lindelof implies things about primes, and also (like RH) has lots of implications about lots of interesting prime-like (irreducible) objects in different spaces.
Re: Mathematician-M.D. claims to have solved the 110-year-old Lindelöf hypothesis
#8I'm skeptical
Re: Mathematician-M.D. claims to have solved the 110-year-old Lindelöf hypothesis
#9What exactly is the application for cyber security? How does this affect cryptography?
Pretty much all of the relationship to practical stuff in papers like this related to the RH are "it gives us information about the prime numbers, and those are used in cryptography".
It's really just about getting people to perk their ears up rather than true implications about crypto.
Re: Mathematician-M.D. claims to have solved the 110-year-old Lindelöf hypothesis
#10Speaking as an analytic number theorist, the branch of math of which the Lindelof Hypothesis is part:
This is a huge deal, if true. But USC's PR machine seems to have jumped the gun.
The paper in question, found here
https://arxiv.org/pdf/1708.06607.pdf
has so far only been posted to the arXiv (and only eight days ago). It has presumably not been subjected to any sort of peer review yet. No third party other than USC has announced the results. There's no chatter among my mathematician friends, or on the blogosphere.
Fokas's results could be correct. If the community comes to a consensus that they are, this would be a tremendous advance, and the analytic number theory community as a whole will be trumpeting them.
But, for the time being, I stipulate that some small technical error is probably lurking in the details, which would take hours to find, and which will tank the proof.
I hope that I am proven wrong. Until then I propose the headline: "Mathematician-M.D. claims to have solved one of the greatest open problems".