Chapter 869: The Mystery Behind the Quantum World

As the debate surrounding the quasi-Riemann conjecture finally settled, the editorial department of "Annual Mathematics" sent Lu Zhou's mailbox the shortest possible time after receiving Lu Zhou's submission of the paper mail.

In the email, the editorial department of "Annual of Mathematics" first told him that the paper he submitted had successfully passed the "peer review" process. The proof of the "Riemann Hypothesis" was published in a separate special issue, which was used to publish his more than 30-page paper and the unique mathematical tool "super ellipse analysis" used in it.

Generally speaking, only when a major mathematical proposition achieves breakthrough results, it is possible for the "Annual of Mathematics", one of the four top journals, to issue a special issue to publish this paper.

And the quasi-Riemann conjecture is undoubtedly worthy of this honor for its weight in the field of analytical number theory.

And at the same time, considering that the hyperelliptic curve analysis method may play an inspiring role in the research on Riemann's conjecture, and that if you do not master this mathematical tool, you may not be able to understand part of the process in the paper, so the editor of "Annual Mathematics" The Ministry then made the decision to publish the two papers together in the same special issue.

Lu Zhou didn't particularly care about the arrangement of the editorial department of the "Annual of Mathematics". Whether they planned to separate the publications or merge them together to produce a special issue, it had no effect on him.

Perhaps the topic surrounding the quasi-Riemann conjecture may not gradually subside until the beginning of next year. Maybe it will not be until the end of next year that the mathematical community will gradually popularize the mathematical ideas he used in proving the quasi-Riemann conjecture.

But for Lu Zhou himself, since this proposition was proved by him, it is already a thing of the past.

What's more, he had already posted the preprint on Arxiv before, and now at least half of the scholars in the mathematics field have read the preprint he posted on Arxiv, and what he expected has been completed.

All that remains for him to do is to further extend the results of the Quasi-Riemann Hypothesis to the "True Riemann Hypothesis"...

It is worth mentioning that in the three days since the preprint was released, it seems that people have continuously made breakthroughs in the value of ε.

And this number has also changed from the initial infinitesimal to a finite value.

According to the data on Arxiv and the statistics of mathematics gossip forums such as Mathoverflow, the value of ε is being refreshed every day or even every hour, making great strides in the direction of 1/2.

As of now, this number has been refreshed to one in 60 million.

Just when almost half of the mathematics world was frantically participating in this "mathematical competition" to find a larger ε, a ridiculous thing happened at the same time.

As we all know, papers are time-sensitive.

Whoever completes a successful research first, the research results will belong to whoever. However, due to the academic rigor of journals, the review cycle is usually very long, so many people will choose to post preprints to occupy the pit.

However, posting preprints cannot solve all problems once and for all. For example, if you just made a successful research with ε=0.01, and others have already achieved ε=0.1, then after his research results are released, your research will lose its registration. value of publication.

This is good news for the mathematics community, but it is undoubtedly a disaster for a doctor who needs a thesis to graduate.

Therefore, after posting their research results on Arxvi, almost everyone expects to publish their results as soon as possible, even choosing some less famous journals with a shorter review period.

Unfortunately, since these papers quoted part of the hyperelliptic geometric analysis method proposed by Lu Zhou, Lu Zhou's own papers were still in the review stage, so there was no way to mark the references.

What?

You mean the preprint that Lu Zhou posted on Arxiv?

Needless to say, most regular journals and reviewers are stubborn and refuse to cite "non-peer-reviewed" preprints in their papers. However, if you directly use the results on Arxiv without citations, you may be suspected of plagiarism.

Therefore, such a dumbfounding scene happened.

Everyone knows that this conclusion is correct, but no one can use it.

Many people had no choice but to post their papers as preprints after finishing their papers. At the same time, they paid close attention to the trend of "Annals of Mathematics" and tried to publish Lu Zhou's papers. The first time to submit your own paper.

This is probably the first time that the publication speed of journals has been left behind by the speed of scientific research...

...

On the other side, Lu Zhou, who saw off his old friends, boarded the SUV parked at the gate of the airport and returned to Zhongshan International's villa.

Although the entire mathematics world is like a gold rush, and scholars in almost all related fields are devoted to the exploration of the value of ε, Lu Zhou is not particularly interested in the study of the value of ε.

If it is not possible to directly advance ε to 1/2, there is a high probability that the final result will be the same as the original research on the twin prime number conjecture. No matter how skillfully the hyperelliptic curve is selected on the complex plane, it will only be infinitely close to 1/2 in the end. 2, without being able to skip the last step.

During this period of time, apart from occasionally paying attention to whether anyone on Arxiv has made groundbreaking results with his hyperelliptic curve analysis method, or developed any new gameplay, he has relied on the resources of Jinling University, Collect important documents about the Riemann Hypothesis all over the world.

It is a taboo to work behind closed doors when research is stuck in a bottleneck. Only by getting in touch with some novel ideas, or communicating with scholars in the same field, can sparks of ideas be sparked.

It is precisely because of this that the gift that Professor Faltings gave him before he left is very precious...

After returning home, he went straight to the study and sat down. Lu Zhou couldn't wait to take out the notebook and spread it on the table.

As Terence Tao said, many interesting ideas are recorded in this notebook.

Some of them have been tested by Professor Faltings himself and proved to be unworkable, and some are simply pure imagination, or he feels a little hopeful, but it is too late to try.

If this notebook is in the hands of others, it may not be easy to understand it.

But for Lu Zhou, it was exactly what he needed most!

Flipping through the notes line by line, Lu Zhou's eyes gradually became excited, but when he turned to the corner of a page, he suddenly froze for a moment.

Different from the previous fragmented records, on this folded page, there are rows of neat handwriting. Unlike the content of the first half, the content of this part is written in German.

Lu Zhou doesn't speak German, but fortunately, Xiao Ai is here.

With the help of Xiaoai, he easily completed the translation of this page.

Surprisingly, the content of this page is not a description of any academic achievements, but rather an article...

journal?

[While studying Professor Hilbert's thesis, I found an interesting guess in his writings. If the non-trivial zeros of the Riemann zeta function are written in the form of ρ=1/2+it, then those t correspond one-to-one to the eigenvalues ​​of some Hermitian operator. If this conjecture is true, then the Riemann operator should be a special random Hermitian matrix. 】

[During afternoon tea at the Max Planck Society, I had a serious discussion with Professor Klitzing from the Institute of Physics, and we were all taken aback by our own discoveries. 】

[Surprisingly, a purely mathematical problem such as the Riemann zeta function is actually related to quantum mechanics! Afterwards, I exchanged this issue with Edward Witten in an email, but unfortunately nothing useful was discussed. 】

[If I had taken quantum mechanics as an elective before, it would be too late for me to study physics now...]

The index finger slid across the traces of the folded corners, and Lu Zhou, who gently put down the note, gradually began to show a trace of shock on his face.

Not 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, and even communicated with another old friend of his, Professor Klitzing, and Edward Witten, a big cow in the field of theoretical physics. past this question.

Unfortunately, although they all realized the inextricable connection among them, they failed to dig out the secret behind it.

What exactly does this mean?

If the non-trivial zero point of the ζ function corresponds to the energy level of a certain quantum mechanical system, the whole of the non-trivial zero point corresponds to the energy spectrum of the quantum mechanical system, and the Hamiltonian of this system is called the Riemann operator. If the Riemann conjecture is true... what kind of mysterious quantum mechanical system will it correspond to?

Conversely, if it is possible to find a Hermitian operator whose entire eigenvalues ​​correspond to the non-trivial zeros of the Riemannζ function, or to put it more simply, does finding such a "Riemannian system" also mean that it can be obtained from physics Prove the Riemann Hypothesis from a scientific point of view?

The expression of interest on Lu Zhou's face became more and more intense.

Although he is more inclined to reveal the physical meaning behind the Riemann conjecture through purely mathematical research, this does not prevent him from being shocked by everything in front of him and the tip of the iceberg revealed from the unknown mystery.

Two unrelated parallel lines, after spanning a century and a half, unexpectedly converged.

In the distant nineteenth century, there was no such thing as quantum mechanics, but there was such a function that could echo it...

At this moment, the phone on the corner of the table rang suddenly, interrupting Lu Zhou's thoughts.

Reaching out to pick up the phone, Lu Zhou pressed the on button and brought it to his ear.

Just when he was about to say "Hello" impatiently, the person on the other end of the phone spoke first.

With a bit of embarrassment, the person on the other end of the phone coughed lightly.

"...Well, Academician Lu, do you remember me?"