Can Qiao Yu’s method solve this problem?”

After making coffee, Peter Sarnak took the initiative to say.

The Selberg Hypothesis can be regarded as a special case of the generalized Riemann Hypothesis. Its mathematical expression is that the non-trivial zero points of all automorphic L-functions on the key strip 0
(s)=1/2.

Because this conjecture covers all automorphic L-functions, including the Riemann ζ function and the Dirichlet L-function, it is also a subset of the generalized Riemann conjecture.

In the history of mathematics, there have always been people who like to raise some strange but significant questions.

The Selberg Hypothesis is undoubtedly one of them. Although it is not as well-known as the Riemann Hypothesis, its significance is also far-reaching.

For example, it inspired research on modular forms, automorphic forms and spectral theory, and was even crucial to the Langlands Program.

Of course, because of this, the Selberg Hypothesis relies on higher-level tools and the research threshold is very high, so there are relatively few researchers. In addition, the history is not as long as the Riemann Hypothesis, so the popularity is naturally not that high.

Zhang Shuwen shrugged, and then replied: "How should I answer your question? Well, Peter, theoretically I can answer you for sure, yes!

But at present, I still have no idea how to operate it. I believe you should have read the relevant literature before asking this question! Although there are many related papers, most of them are still very shallow.

In fact, we are the same. Qiao Yu's theory is still at a stage that needs to be fully developed. As I said in class, there are still many articles to be done on this axiom system."

Peter Sarnak smiled and said: "See, this is exactly why I came to talk to you. I went to see Professor Dugan this morning, hoping that he could help me introduce him.

I think we can work with Qiao Yu to solve this problem. You know the significance of this topic. But Professor Dugan said maybe I can talk to you."

Zhang Shuwen was stunned, and then looked at Peter Sarnak doubtfully and asked: "You can send an email directly to Qiao Yu. I think if he is interested, he should reply to you, right? I have met that kid, and he is still very worried.

Polite."

Peter Sarnak spread his hands and laughed at himself: "Maybe it's because I'm not well-known. I wrote him three emails, all of which were automatic replies. I doubt he has the habit of checking his mailbox at all."

Zhang Shuwen really didn't know about this situation. He hadn't contacted Qiao Yu recently.

He originally planned to wait until March to visit Huaqing, and then discuss with Qiao Yu how the generalized modal system could be better integrated into the number theory system.

"Well, let me ask you. Of course, I'm not sure that he is interested in this proposition. I heard that he has been quite busy recently and has at least two collaborative research projects on hand."

Zhang Shuwen thought for a while and agreed.

"Thank you, Zhang! By the way, help me tell Qiao Yu that I am very interested in his theory. If he agrees, I can share all the current research data with him.

You know, although we are still some way away from the final solution to the Selberg Conjecture, we have still done some breakthrough work.

For example, we have verified several special cases of zero-point distribution on some specific types of automorphic L-functions, and studied the analogy of zero-point distribution in random matrix theory.

Especially the Berry-Keating model, in short, I believe that this preliminary work should provide some help for the mapping of modal space." Peter Sarnak said confidently.

Zhang Shuwen nodded.

"By the way, tell him that if his method can really help us solve this problem, we can work together."

Peter Sarnak explained again.

There is no way.

Just like many unsolved mathematical problems, the reason why they cannot be effectively solved is mostly because the existing mathematical tools cannot explore the truth at all.

I have been thinking about a certain mathematical problem for more than ten or even decades, and basically I have tried all the tools that can be used.

Zhang Shuwen expressed his understanding, but he would definitely not take over everything. There was no way, Qiao Yu was not his student. It was even difficult to reconcile the relationship between the two.

After all, when the two met for the first time, he severely punished Qiao Yu and even criticized him for not being too ambitious.

Although he did have good intentions at the time, there is a deep gap between today's young people and his generation. Zhang Shuwen didn't know what Qiao Yu was thinking.

Maybe I have been slandering him as an old man who is good at teaching others - this is very possible. Especially since this guy has grown into a genius so quickly that he is no longer easy to evaluate...

This is even more embarrassing. But even if we go back to the first time the two met, Zhang Shuwen felt that what should be said at that time still had to be said. He could not let the trajectory of fate change...

If he had not said that, Qiao Yu would not have constructed the generalized modal axiom system, which would definitely be a great loss to the mathematical community.

Recalling the scene of his first meeting with Qiao Yu, Zhang Shuwen nodded absently and promised: "Don't worry, I will convey the original words to him."

"Thank you, Zhang! I'm waiting for your news."

After speaking, Peter Sarnak couldn't help but look at his cup of coffee that had not been touched much, and commented seriously: "You should protest to Professor Dugan and change the coffee.

This kind of coffee is sour and astringent, I really don’t know how you can tolerate it. Next time you come to the institute, trust me, the coffee there is much better than your garbage coffee.”

Zhang Shuwen smiled.

This guy is not the first person to complain about the bad free coffee at Mathematics College, and he certainly won't be the last.

After sending Peter Sarnak away, Zhang Shuwen sat in the tea room and thought for a while before returning to his office and dialing Yuan Zhengxin's phone number from the office phone.

"Hey, is this Shuwen?"

"Yes, hello Mr. Yuan, how are you doing lately?"

"It's not bad. I can still eat. I should be fine for another ten years."

Listening to Yuan Zhengzhong's angry voice on the phone, Zhang Shuwen subconsciously smiled.

It's not surprising to hear that the old man is in a good mood. Although there are still many disputes between the two parties, with a genius like Qiao Yu acting as lubricant in the middle, it is reasonable to be happy.

After a person has passed the age of knowing his destiny, he actually doesn’t want much. With Mr. Yuan’s status, it is obviously the most important thing to inherit his knowledge.

He had heard about it at Princeton. Not only was Qiao Yu very talented in mathematics, but Qiao Yu's mother seemed to be very talented as well. She was just a little older. It was a pity, but it was said that there was not much of a problem in inheriting the mantle.

"Take care of yourself." Zhang Shuwen said sincerely.

"What's the matter with Shuwen calling at this time? It's already nine o'clock in the evening at Princeton, right? It's still in the office."

Zhang Shuwen said quickly: "Professor Sarnak just talked to me specifically. He also spent a lot of thought on Selberg's conjecture, and it has been stuck in a bottleneck for a long time.

During this period, I came across Qiao Yu’s method and was very interested. I wanted to invite Qiao Yu to collaborate on this topic, but I sent Qiao Yu three emails but never received a reply.

So you came to me here and thought about asking me to help ask if Qiao Yu didn't read the email. If possible, I still hope to promote this cooperation."

After saying this, Zhang Shuwen said nothing. To his surprise, Mr. Yuan on the opposite side didn't speak immediately either, and the phone fell into silence.

Zhang Shuwen did not urge him, he just waited quietly, but he began to have doubts in his heart. To be honest, this was not a very excessive request. Whether he agreed or refused, given Mr. Yuan's temperament, he should be very happy.

There was silence for nearly thirty seconds. Just as Zhang Shuwen was about to speak to break the silence, Yuan Zhengxin spoke up: "Shuwen, have you thought about coming back recently?"

Such a heavy topic, Zhang Shuwen thought about it for a few seconds and then asked: "You mean resigning from your teaching position at Princeton?"

"Yes, come back and teach in Huaqing. I can't work for a few more years. Come and help me look after the Mathematics Research Center and look at Qiao Yu. This kid is too young after all. I'm not worried about mathematics, but there are other issues.

It's still not clear enough.

There has to be someone who keeps an eye on him and doesn't let him go astray. I don't trust Tian Yanzhen. Really, without a child like Qiao Yu, I wouldn't advise you like this. But you think, now even your colleagues

They all look forward to cooperating with him. What does that mean?

Do you dare to imagine? In the near future, China will develop from a big country in mathematics to a powerful country in mathematics? Or even become the center of the world's academic community? Perhaps China's national strength could not support such a grand vision before, but what about now?

Think again about the current relationship between China and the other side. Shuwen, think about it carefully! Maybe the vision of our generation can be realized in Qiao Yu’s generation!

History is a cycle of reincarnations, and I have a hunch that another era of technological explosion may be about to begin. In this round, our national strength is no worse than any other country, and we even have many advantages that other countries do not have!"

Zhang Shuwen could feel that Yuan Zhengxin's heart was surging when he said these words. After thinking seriously for a moment, his heart began to waver.

He just put down everything he had here and went back directly, but hesitantly.

After thinking for a moment, he said: "Yuan Laorong, I will think about it."

"Well, this is a big deal, and you need to think about it. As for the matter you mentioned, I will talk to Qiao Yu. But don't have high hopes. There is a reason why he doesn't reply to emails.

Recently, many teams and organizations have invited him to cooperate. The little guy is a little unbearable and even complained to me some time ago. And he does have a lot of things going on recently. You have to understand."

Zhang Shuwen replied: "Understood. I'm just asking questions for Peter. Naturally, Qiao Yu still has to put his own plans first."

"Okay, think carefully about what I just mentioned. Once you make a decision, let me know as soon as possible."

"Okay, Mr. Yuan."

After hanging up the phone, Zhang Shuwen sat there in a daze for a while. In front of Mr. Yuan, he was a junior, but really speaking, he was sixty-one this year.

Whether or not to go back at this age is indeed a question. After thinking for a while, Zhang Shuwen's eyes focused on the courseware on the table.

There was a paper underneath the courseware. Zhang Shuwen subconsciously took out the paper and flipped through a few pages at random.

This is exactly the paper Qiao Yu published in the Annals of Mathematics.

The blank spaces at the top and sides of almost every page are densely filled with various annotations, ideas, and additional derivation processes.

It is only a vision for China to become a powerful country in mathematics, but it would be true to be able to come into contact with the most cutting-edge mathematical ideas if we go back.

A huge system that converts all numbers into elements, it’s a shame that guy can think of it and can do it.
Chapter completed!