The controversy surrounding the quasi Riemann's conjecture finally settled. After the Annual Mathematics editorial department received Lu Zhou's "hyperelliptic curve analysis" thesis, they immediately sent an email to Lu Zhou's email.
In the email, the Annual Mathematics editorial department first told him that his previous thesis had successfully passed the "peer review" stage. At the end of the month, Annual Mathematics would publish a special issue dedicated to the proof of the quasi Riemann's conjecture. It would be used to publish his 30-page thesis and the unique mathematical tool, the "hyperelliptic curve analysis".
Generally speaking, only when a major mathematical proposition had a breakthrough result would it be possible for Annual Mathematics, one of the top four journals, to publish a special issue of the thesis.
The weight of the Quasi Riemann hypothesis in the analytic number theory community was undoubtedly worthy of this honor.
Also, considering that the hyperelliptic curve analysis method might play an inspiring role in the research of the Riemann's conjecture, and that it might be difficult to understand the process of the thesis without mastering this mathematical tool, the Annual Mathematics editorial department decided to publish the two theses together in the same special issue.
Lu Zhou didn't particularly care about the arrangement of the Annual Mathematics editorial department. It didn't matter to him whether they planned to publish the two papers separately or publish a special issue together.
Perhaps the discussion surrounding the quasi Riemann's conjecture would gradually die down at the beginning of next year. Perhaps by the end of next year, the mathematics community would be able to slowly popularize the mathematical ideas that he used in proving the quasi Riemann's conjecture.
However, for Lu Zhou, ever since he proved the conjecture, it had become a thing of the past.
Not to mention, he had already posted the preprint on arXiv. Now, at least half of the mathematics community had read his preprint on arXiv. He had accomplished his goal.
All he had to do now was to further extend the results of the quasi Riemann's conjecture to the true Riemann's conjecture …
It was worth mentioning that in the three days since the preprint was released, people seemed to have made breakthroughs in the value of epsilon.
This number went from being infinitesimal to having a finite value.
According to the data on arXiv and Mathoverflow, the value of epsilon was being updated every day, even every hour. It was moving towards 1/2.
As of now, this number had been refreshed to one in sixty million.
Almost half of the mathematics community was crazily participating in this "mathematics competition" to find a larger epsilon. At the same time, something ridiculous happened.
As we all know, the timeliness of a thesis is important.
The research results belonged to whoever completed the research first. However, due to the academic rigor of journals, the review cycle was usually very long. Therefore, many people would choose to put up preprints.
However, publishing a preprint couldn't solve all problems once and for all. For example, if you had just successfully achieved epsilon = 0.01, and someone else had already achieved epsilon = 0.1, then after that person's research was published, your research would lose the value of being published in the journal.
This was a good thing for the mathematics community, but it was undoubtedly a disaster for a PhD student who needed a thesis to graduate.
Therefore, after posting their research results on arxvi, almost everyone wanted to publish their results as soon as possible. Some people even chose journals that weren't as famous and had a shorter review cycle.
Unfortunately, because these theses cited part of the hyperelliptic geometric analysis method proposed by Lu Zhou, Lu Zhou's own thesis was still in the review stage, so there was no way to cite it.
What?
You mean Lu Zhou's preprint on arXiv?
Needless to say, most journals and reviewers were very stubborn. They would refuse to cite a "non-peer-reviewed" preprint in their thesis. However, if one didn't cite it and directly used arXiv's results, they would be suspected of plagiarism.
Therefore, such a hilarious scene unfolded before everyone's eyes.
Everyone knew that this conclusion was correct, but no one could use it.
Many people couldn't submit their theses after they finished them. They could only put up their own theses as preprints. At the same time, they paid close attention to Annual Mathematics and tried to submit their own theses as soon as Lu Zhou's thesis was published.
This was probably the first time that the speed of a journal's publication was left behind by the speed of scientific research …
…
On the other hand, Lu Zhou saw off his old friends. He sat in his SUV parked at the airport and returned to his Zhongshan International mansion.
Even though there was a gold rush in the mathematics community, and almost all scholars in related fields were invested in exploring the value of epsilon, Lu Zhou wasn't particularly interested in studying the value of epsilon.
If he couldn't directly push epsilon to 1/2, the final result would be the same as the twin prime conjecture. No matter how cleverly he chose the hyperelliptic curve on the complex plane, he would only be infinitely close to 1/2. He wouldn't be able to take the final step.
During this time, other than occasionally paying attention to arXiv to see if anyone used his hyperelliptic curve analysis method to create groundbreaking results, he would use the resources of Jin Ling University to search for important literature on Riemann's conjecture.
When one's research was at a bottleneck, it was a taboo to work behind closed doors. Only by interacting with new ideas or communicating with other scholars in the same field would one be able to spark new ideas.
Because of this, the gift that Professor Faltings gave Lu Zhou before he left was extremely precious …
When Lu Zhou returned home, he went straight to his study room and sat down. He couldn't wait to take out the notebook and spread it out on the table.
Just as Tao Zhexuan said, there were many interesting thoughts recorded in this notebook.
Some of them had been tested by Professor Faltings himself and proved to be unfeasible. Some of them were just ideas that Tao Zhexuan thought had some hope, but he didn't have the time to try them.
If someone else had this notebook, they probably wouldn't be able to understand it.
But for Lu Zhou, this was what he needed the most!
Lu Zhou flipped through the notes line by line, and his eyes gradually stained with a hint of excitement. However, when he flipped to the corner of a page, he suddenly paused for a second.
Unlike the previous fragmented records, there were neat lines of words printed on this folded page. Unlike the first half of the notebook, this part was written in German.
Lu Zhou didn't speak German, but fortunately, he had Xiao Ai with him.
With the help of Xiao Ai, he easily translated the contents of this page.
Surprisingly, the content of this page wasn't an academic record. Instead, it was like a …
Diary?
[When I was studying Professor Hilbert's thesis, I found a very interesting conjecture in his work. If the non-trivial zeros of the Riemann zeta function are written in the form of ρ = 1/2 + it, then those t correspond to the eigenvalues of a certain Hermitian operator. If this conjecture is correct, then the Riemann operator should be a special random Hermitian matrix.
[During afternoon tea at the Max Planck Institute, I seriously discussed this problem with Professor Klitzing from the Institute of Physics. We were both shocked by our findings.
[Surprisingly, a pure mathematical problem like the Riemann zeta function is actually related to quantum mechanics! After that, I discussed this issue with Edward Witten in an email, but unfortunately, we didn't discuss anything useful.]
[If only I had taken quantum mechanics as an elective before. I'm afraid it's too late for me to study physics now …]
Lu Zhou gently slid his index finger across the corner of the notebook. He gently put down the notebook and began to look shocked.
It wasn't just Montgomery and Professor Dyson …
Professor Faltings, who was far away in Germany, also noticed the projection of the Riemann zeta function in quantum physics. He even discussed this issue with his old friend, Professor Klitzing, as well as with Edward Witten.
Unfortunately, even though they all realized the inextricable connection, they failed to dig out the secret behind it.
What did this mean?
If the non-trivial zeros of the zeta function corresponded to the energy level of a quantum mechanical system, then the non-trivial zeros corresponded to the energy spectrum of the quantum mechanical system. If the Hamiltonian of this system was called the Riemann operator, then if the Riemann conjecture was true … What kind of mysterious quantum mechanical system would it correspond to?
Conversely, if one could find a Hermitian operator whose eigenvalues corresponded to the non-trivial zeros of the Riemann zeta function, then would such a "Riemann system" be able to prove the Riemann conjecture from a physical point of view?
The look of interest on Lu Zhou's face became more and more intense.
Even though he was more inclined to reveal the physical meaning behind the Riemann conjecture through pure mathematical research, this didn't prevent him from being shocked by what he was seeing.
Two parallel lines that had nothing to do with each other actually converged after a century and a half.
In the 19th century, quantum mechanics didn't exist, but there was a function that resonated with it …
Suddenly, the phone on the corner of the table began to ring, interrupting Lu Zhou's thoughts.
Lu Zhou picked up the phone and pressed the answer button. He then put the phone next to his ear.
Just as he was about to impatiently say "hello", the person on the other end of the phone spoke first.
The person on the other end of the phone coughed awkwardly.
"Um, Academician Lu, do you still remember me?"
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