<p>A recent <a href="https://viterbischool.usc.edu/news/2018/06/mathematician-m-d-solves-one-of-the-greatest-open-problems-in-the-history-of-mathematics/" rel="noreferrer">press release</a> from the Viterbi School of Engineering at USC discussed the proof of the Lindelöf hypothesis by Athanassios Fokas, a visiting professor from the Department of Applied Mathematics and Theoretical Physics at the University of Cambridge.</p>

<p>In the press release, it is noted that the proof has implications for computational complexity theory and quantum computing, but no real details are provided. I've skimmed the paper on <a href="https://arxiv.org/abs/1708.06607" rel="noreferrer">arXiv.org</a>, but I don't believe such implications are noted and (unfortunately) mathematical proofs are not my area of expertise.</p>

<p>So, as stated, my question is: <strong>How would a proof of the Lindelöf hypothesis improve our understanding of computational complexity classes?</strong> I'm especially interested in any refinements that relate to quantum computing (assuming they do in fact exist).</p>

CC BY-SA 4.0
2018-06-29T10:33:40.470Z
Good question, probably triggered by https://mathoverflow.net/questions/303888/lindelof-hypothesis-claim. However, that question correctly labels that press release as a "puff piece"... The current arXiv version no longer claims a proof. Even the non-extended Riemann hypothesis has nearly no known implications on complexity classes. Probably asking on MO about the "Lindelöf implies most of the claims of Riemann and Riemann fully implies Lindelöf, therefore a proof of Lindelöf equals a major breakthrough in the field of mathematics." claim would have produced more illuminating answers...
Thomas Klimpel
CC BY-SA 4.0
2018-06-30T19:31:25.790Z
Thank you for the clarification - it’s a shame that the press release is so puffed, but not altogether surprising I suppose. It’s especially confusing considering the recent date of the press release (June, 2018) and the more recent preprint on arXiv (which lacks any of the assertions made). Anyway, I actually didn’t see the mathoverflow question, the press release popped up in my HackerNews feed - should have searched that exchange too. If you write up your comment as an answer I’ll go ahead and accept it.
Greenstick
<cc.complexity-theory><quantum-computing><time-complexity><quantum-information><proofs>
How would proof of the Lindelöf hypothesis improve our understanding of computational complexity classes?
Greenstick
# How would proof of the Lindelöf hypothesis improve our understanding of computational complexity classes?

(Asked by: username_0 on 2018-06-29)

A recent [press release](https://viterbischool.usc.edu/news/2018/06/mathematician-m-d-solves-one-of-the-greatest-open-problems-in-the-history-of-mathematics/) from the Viterbi School of Engineering at USC discussed the proof of the Lindelöf hypothesis by Athanassios Fokas, a visiting professor from the Department of Applied Mathematics and Theoretical Physics at the University of Cambridge.

In the press release, it is noted that the proof has implications for computational complexity theory and quantum computing, but no real details are provided. I've skimmed the paper on [arXiv.org](https://arxiv.org/abs/1708.06607), but I don't believe such implications are noted and (unfortunately) mathematical proofs are not my area of expertise.

So, as stated, my question is: **How would a proof of the Lindelöf hypothesis improve our understanding of computational complexity classes?** I'm especially interested in any refinements that relate to quantum computing (assuming they do in fact exist).

**Tags:** cc.complexity-theory, quantum-computing, time-complexity, quantum-information, proofs
> **Comments:**
> **username_1**: Good question, probably triggered by https://mathoverflow.net/questions/303888/lindelof-hypothesis-claim. However, that question correctly labels that press release as a "puff piece"... The current arXiv version no longer claims a proof. Even the non-extended Riemann hypothesis has nearly no known implications on complexity classes. Probably asking on MO about the "Lindelöf implies most of the claims of Riemann and Riemann fully implies Lindelöf, therefore a proof of Lindelöf equals a major breakthrough in the field of mathematics." claim would have produced more illuminating answers...  
> **username_0**: Thank you for the clarification - it’s a shame that the press release is so puffed, but not altogether surprising I suppose. It’s especially confusing considering the recent date of the press release (June, 2018) and the more recent preprint on arXiv (which lacks any of the assertions made). Anyway, I actually didn’t see the mathoverflow question, the press release popped up in my HackerNews feed - should have searched that exchange too. If you write up your comment as an answer I’ll go ahead and accept it.  

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## 0 answers

