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Message boards : General discussion : Lindelöf hypothesis formally proved

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recoil44Project donor
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Message 119103 - Posted: 28 Jun 2018 | 15:43:59 UTC

Put forth in 1908 by Finnish topologist Ernst Leonard Lindelöf, the Lindelöf hypothesis is a conjecture about the rate of growth of the Riemann zeta function on the critical line implied by one of the most famous unsolved problems related to prime numbers, the Riemann Hypothesis, popularly referred to as the Holy Grail of math.

https://viterbischool.usc.edu/news/2018/06/mathematician-m-d-solves-one-of-the-greatest-open-problems-in-the-history-of-mathematics/

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Discovered 3 mega primesFound 1 prime in the 2018 Tour de PrimesFound 2 primes in the 2020 Tour de PrimesFound 2 primes in the 2021 Tour de Primes321 LLR Bronze: Earned 10,000 credits (38,954)ESP LLR Gold: Earned 500,000 credits (942,185)PPS LLR Double Silver: Earned 200,000,000 credits (284,953,062)PSP LLR Silver: Earned 100,000 credits (489,641)SoB LLR Jade: Earned 10,000,000 credits (12,960,428)SR5 LLR Jade: Earned 10,000,000 credits (10,694,695)SGS LLR Gold: Earned 500,000 credits (563,819)TRP LLR Jade: Earned 10,000,000 credits (19,078,708)321 Sieve (suspended) Silver: Earned 100,000 credits (395,205)PPS Sieve Double Silver: Earned 200,000,000 credits (229,814,554)TRP Sieve (suspended) Gold: Earned 500,000 credits (669,191)AP 26/27 Sapphire: Earned 20,000,000 credits (25,547,717)GFN Double Bronze: Earned 100,000,000 credits (100,995,075)WW Double Amethyst: Earned 1,000,000,000 credits (1,304,292,000)PSA Ruby: Earned 2,000,000 credits (3,025,234)
Message 119105 - Posted: 28 Jun 2018 | 17:49:10 UTC - in response to Message 119103.

"first published on arXiv" usually doesn't bode well for a proof, right? I'd expect an important result like this to be clamored over in other journals and arXiv, historically, seems to be the grounds for amateurs and crackpots.

Though, I suppose Viterbi seems to be a source where reputation is important, and Dr. Fokas does seem to have a measurable amount of respect from his peers from the sources I've found. Perhaps this is legitimate and, from the book I read about the Riemann Hypothesis, would have far-reaching and influencial consequences.

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Discovered 1 mega primeFound 1 prime in the 2019 Tour de PrimesFound 1 mega prime in the 2019 Tour de Primes321 LLR Turquoise: Earned 5,000,000 credits (5,019,377)Cullen LLR Turquoise: Earned 5,000,000 credits (5,064,170)ESP LLR Turquoise: Earned 5,000,000 credits (5,001,303)Generalized Cullen/Woodall LLR Turquoise: Earned 5,000,000 credits (5,094,139)PPS LLR Turquoise: Earned 5,000,000 credits (6,021,807)PSP LLR Turquoise: Earned 5,000,000 credits (5,085,124)SoB LLR Turquoise: Earned 5,000,000 credits (5,042,051)SR5 LLR Turquoise: Earned 5,000,000 credits (5,077,248)SGS LLR Turquoise: Earned 5,000,000 credits (5,000,448)TRP LLR Turquoise: Earned 5,000,000 credits (5,003,404)Woodall LLR Turquoise: Earned 5,000,000 credits (5,035,352)321 Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,061,436)Generalized Cullen/Woodall Sieve (suspended) Jade: Earned 10,000,000 credits (10,012,148)PPS Sieve Double Bronze: Earned 100,000,000 credits (108,556,313)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Ruby: Earned 2,000,000 credits (2,089,865)TRP Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,297,782)AP 26/27 Emerald: Earned 50,000,000 credits (50,153,415)GFN Double Bronze: Earned 100,000,000 credits (106,065,222)PSA Emerald: Earned 50,000,000 credits (67,666,890)
Message 119121 - Posted: 29 Jun 2018 | 11:45:13 UTC - in response to Message 119105.

Basically my brain saw "Historical Math Proof" and "Prime Numbers" so I posted the link.

I think you're right, if it was legit there would be a lot more press. Could be waiting for peer reviews or something, I haven't looked into this any further than skimming the article. I'm not a math guy but I know there are plenty in the PG community.

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Message 119128 - Posted: 29 Jun 2018 | 14:53:05 UTC

As far as I can see, the current version of the preprint, in the abstract (the only thing I have read), says only:

Hence, since the above identity is valid for all ϵ, this asymptotic identity suggests the validity of Lindelöf's hypothesis. The completion of the rigorous derivation of the above results will be presented in a companion paper.
That does not sound like a claim of a proof.

The Wikipedia page Athanassios S. Fokas currently says:
In 2017, Fokas briefly claimed a proof of the Lindelöf Hypothesis. The preprint has since been updated and the claim withdrawn.


/JeppeSN

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Message 119152 - Posted: 30 Jun 2018 | 18:31:01 UTC

I'm not really qualified to comment on the mathematics or its implications, but there is nothing here that cries "crackpot". Indeed, a professor with joint appointment at Cambridge, with mainstream funding (EPSRC) and a host of reliable collaborators acknowledged at the end is all indicative of "good science". Publishing on Arxiv is becoming more and more of the norm as it encourages early review by many eyes and the paper (or the companion referred to) may eventually make it to print in a mainstream journal.

- Iain
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Found 1 prime in the 2020 Tour de Primes321 LLR Gold: Earned 500,000 credits (529,293)Cullen LLR Gold: Earned 500,000 credits (611,298)ESP LLR Silver: Earned 100,000 credits (174,818)Generalized Cullen/Woodall LLR Bronze: Earned 10,000 credits (35,236)PPS LLR Jade: Earned 10,000,000 credits (13,193,892)PSP LLR Silver: Earned 100,000 credits (428,457)SoB LLR Silver: Earned 100,000 credits (466,812)SR5 LLR Silver: Earned 100,000 credits (145,419)SGS LLR Silver: Earned 100,000 credits (112,277)TRP LLR Silver: Earned 100,000 credits (342,501)Woodall LLR Silver: Earned 100,000 credits (109,455)321 Sieve (suspended) Silver: Earned 100,000 credits (175,037)PPS Sieve Bronze: Earned 10,000 credits (10,113)AP 26/27 Bronze: Earned 10,000 credits (12,129)GFN Ruby: Earned 2,000,000 credits (2,059,478)WW Turquoise: Earned 5,000,000 credits (9,640,000)PSA Turquoise: Earned 5,000,000 credits (7,614,290)
Message 119153 - Posted: 30 Jun 2018 | 19:14:28 UTC - in response to Message 119152.

I do not think the author is a crackpot (his affiliations, and he has a Wikipedia article). But on the other hand, he does not seem to claim that he has proved the Lindelöf hypothesis, in the newest version of his arXiv paper. /JeppeSN

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Discovered 3 mega primesFound 1 prime in the 2018 Tour de PrimesFound 2 primes in the 2020 Tour de PrimesFound 2 primes in the 2021 Tour de Primes321 LLR Bronze: Earned 10,000 credits (38,954)ESP LLR Gold: Earned 500,000 credits (942,185)PPS LLR Double Silver: Earned 200,000,000 credits (284,953,062)PSP LLR Silver: Earned 100,000 credits (489,641)SoB LLR Jade: Earned 10,000,000 credits (12,960,428)SR5 LLR Jade: Earned 10,000,000 credits (10,694,695)SGS LLR Gold: Earned 500,000 credits (563,819)TRP LLR Jade: Earned 10,000,000 credits (19,078,708)321 Sieve (suspended) Silver: Earned 100,000 credits (395,205)PPS Sieve Double Silver: Earned 200,000,000 credits (229,814,554)TRP Sieve (suspended) Gold: Earned 500,000 credits (669,191)AP 26/27 Sapphire: Earned 20,000,000 credits (25,547,717)GFN Double Bronze: Earned 100,000,000 credits (100,995,075)WW Double Amethyst: Earned 1,000,000,000 credits (1,304,292,000)PSA Ruby: Earned 2,000,000 credits (3,025,234)
Message 119154 - Posted: 30 Jun 2018 | 21:57:00 UTC

I agree that Fokas seems to be well-grounded and researched in his discovery, and would not call him a crockpot. I was just surprised at his use of arXiv, though if what is being said about arXiv becoming more legitimate and acceptable is true, then I have no doubts that what has been discovered is legitimate as he says it is.

Wikipedia was very quick to jump on the gun about "him claiming a proof", as previous edits of the page indicate. Now it seems the truth is that he has another approach to a proof, with more rigor coming in another paper. Perhaps a full proof of the hypothesis will come soon.

Message boards : General discussion : Lindelöf hypothesis formally proved

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