Listening to Deligne's impatient inquiry, Xu Chuan was not surprised.

He nodded lightly and smiled, "Of course."

While it is an unspoken rule in academia not to ask other scholars about unfinished research, it is clear that he and Drinne are not in this category.

Neither he nor Delgne could have done such a dirty thing.

After a slight pause, Xu Chuan thought about organizing his language and said, "If you want to advance the non-trivial zero point of the Riemann conjecture to 1/2, what you need to do is naturally prove that all the zero points are distributed on the zero boundary. But it's a difficult route to reach the end, and the infinite number of primes separates the two worlds like a barrier to the universe."

"So, in my opinion, instead of working in the non-trivial zero region, it is better to shrink it back to the Jensen inequality and then study it through sub-Sigma algebra......

"Perhaps, this path is a little more promising than the contraction of the critical zone."

"Jensen's inequality...."Deligne thought for a moment, and asked quickly, "Your idea is to regress the prime counting function π(x)?"

Although the Riemann conjecture is not the direction of his research, and it is difficult to think of any new breakthroughs, as a top mathematician, he can still see through the essence of the problem after Xu Chuan put forward his own research ideas.

Xu Chuan nodded and said with a smile: "That's right, the zero point of Reiannζ has an inseparable relationship with prime numbers, the most direct of which is the prime number counting function π (x) can be represented by the zero point of the ζ. The prime counting function is to give the number of prime numbers less than or equal to x, for example π(10)=4, because there are 4 prime numbers less than or equal to 10: 2, 3, 5, 7......

「.... Weierstrass decomposition theorem can be seen as an extension of the fundamental theorem of algebra: that any integer function can be expressed as the product of the function related to its zero point."

During the video call, Xu Chuan and his mentor chatted about the research ideas of the Riemann conjecture.

Opposite, in the park of the Institute for Advanced Study in Princeton, Deligne frowned and pondered.

In the middle of the ring, he raised his head, stared at Xu Chuan with shining eyes, and said, "It is indeed a very interesting path, but how can you solve the problem that the inverse transformation of the integral cannot converge well at the jump of the π(x) function?"

Although analytic number theory is not the main area of his research, he still understands it when he solves Weiy's conjecture.

It may not be as good as G. Faltins and Professor Jean-Pierre Sayre, who specialize in the field of number theory, but from Xu Chuan's analysis, it is not difficult for him to find some big problems that may exist behind this road.

On the other side of the video, Xu Chuan shrugged his shoulders with a smile and said, "There is no good way to do it for the time being."

As Drinne said, there are still many problems in his study of the Riemann conjecture or the solution of the quasi-Riemann conjecture, such as the inverse transformation of the integral that does not converge well at the jump of the π(x) function, which is a problem that needs to be solved.

But this is the Riemann conjecture, and it is normal to have trouble, and it is normal to have problems.

If it had been easy to solve, it would not have been able to survive for a century and a half, and it would have been killed long ago.

Deligne thought for a moment and said, "Maybe it's harder than compressing the critical zone."

Different from the traditional method of studying the Riemann conjecture in the field of mathematics today, the research idea of the regression prime counting function π(x) proposed by Xu Chuan is obviously a new method, or a relatively niche path, at least not many people in the mathematical community today have studied the Riemann conjecture through this method.

In this case, it is impossible to know how many problems may be encountered in front of this road, and the difficulty may be greater than that of compressing the critical zone.

Hearing Deligne's words, Xu Chuan smiled and said, "It's hard or not, it's all there. And..."

"If the Riemann conjecture isn't difficult, I'm not interested in researching it."

It sounds a little crazy, but it's as he says

It is difficult to arouse his interest.

If it is solved casually, then there is no point in his research.

Deligne nodded, not asking anything, but instead said, "If the Riemann conjecture is solved, please remember to tell me as soon as possible."

In fact, he also knows very well that for people like them, once they identify a certain direction, unless they really find something, they will not see the Yellow River and will not die, and they will not hit the south wall and will not look back.

Even, even if they see the Yellow River and hit the south wall, they will stubbornly choose to go in their own direction.

Didn't he, like himself, pursue the basic objects of arithmetic algebraic geometry, and study the standard conjectures left by Grothendieck all his life.

Xu Chuan nodded: "If it can be solved, it will definitely be."

.......

After chatting with Deligne for a while, and asking him for some papers left by his grandfather, Mr. Grothendieck, on the flat and L on the cohomology, non-abelian algebraic geometry, and the duality of continuity and discreteness, Xu Chuan ended the video call.

Although he studied under Professor Pierre de Ligne and was a disciple of the Pope, he did not read all the papers left by Mr. Grothendieck.

Because there are so many.

He founded a whole set of abstract theories of modern algebraic geometry, not to mention the rest, there are more than a dozen masterpieces in the field of algebraic geometry alone.

In addition to algebraic geometry, he is also proficient in topology, abstract algebraic geometry, generalizations, number theory, and many other fields.

Although in the later years of his academic career, he was far away from academia because of his anti-war relations, and all his writings were forbidden to be disseminated to the outside world, but he still left behind a large number of papers and manuscripts.

Perhaps no one else had it, but as one of Mr. Grothendieck's most brilliant protégés, Deligne certainly had a large number of papers and manuscripts in his possession.

And when he was studying abroad at Princeton, he couldn't have read them all.

In addition, he was working on the Hodge conjecture at the time, and he did not have much time to study Grothendieck's writings.

But now, in order to solve the Riemann conjecture, Xu Chuan can only ask his mentor for one more time.

......

When Xu Chuan was flipping through the materials and studying the Riemann conjecture.

On the other hand, on the Arxiv forum, there is an article about p=Np? The conjecture paper quietly set off a storm of discussion in the mathematical community.

The paper is the "Proof of Solving the Polynomial Algorithm for Positive Integer Factorization!" passed on by senior sister Liu Jiaxin! 》

These days, after refining the suggestions and questions that Xu Chuan gave her, she uploaded the paper to Arxiv.

Speaking of which, the mathematics community today is probably influenced by a whole retreat guy, and there are already many scholars who like to upload their papers to Arxiv, a preprint website, when submitting papers.

Even many scholars who didn't like this 'dross' in their eyes are now registered accounts, and even occasionally flip through other people's papers and ideas.

But at the same time, arxiv has also attracted more 'civilian' scholars, throwing one 'outrageous' paper after another on it, hoping to cause some splashes and repercussions and gain some traffic.

In short, mathematics has gradually overwhelmed the computer papers that had become so popular on the arxiv website in the past two years, and once again occupied the top spot on the preprint site.

And such a paper related to the Seven Millennium Problems naturally quickly attracted the attention of others.

The prestigious international mathematical forum athoverFlo

[Have you read the paper on arxiv, "Proof of Solving Large Positive Integer Factorization with Polynomial Algorithm"? 】

[Positive integer factorization problem? p=Np？ Guess? That Professor Xu's? He shot again? 】

[No, the first author of the paper is called Jiaxin Liu, who seems to be also a scholar from Huaguo.] 】

[Liu Jiaxin? I haven't heard of this name (shrugging my shoulders), if it weren't for that Professor Xu, there is a paper on arxiv about this world-class problem, or forget it, are there still few kinds of parallel goods and civil science? 】

[Indeed, arxiv has become more and more mixed in the past two years, although many math masters have registered accounts, but more of them are still many guys who don't understand anything. What Goldbach conjecture papers, what mathematical unification papers are now everywhere, and there are even 1+1 proofs. 】

[No, no, no, this paper is very different, my supervisor has already read it, and he is now working on it, and said that there is a good chance that it really solves the factorization problem of large positive integers. 】

[But not everyone is qualified to say this, dare to ask who is your mentor?] Let me see. 】

[Tao Zhexuan! 】

【......】

......

Scholars at the international mathematical forum athoverFlo have paid attention to things, and the top mathematicians have gradually noticed.

University of California, Los Angeles.

Tao Zhexuan was sitting in his office, flipping through the papers in his hands, his eyes covered by black-rimmed glasses shining brightly.

As a surfer in the world of mathematics, he was probably the first, not to say the first, but definitely the first to discover this paper.

Of course, this also has something to do with his acquaintance with Liu Jiaxin,

At the International Congress of Mathematicians in 18 years, he met the girl, walked with that person at that time, and heard that he also came from the same university, and later chased him to Princeton for further study, and made a lot of achievements related to computer mathematics in Princeton.

Although it is not very famous in the mathematical world, if it is in the computer world, it is actually quite famous.

"It's kind of interesting, this is a reversal of the quadratic sieve factorization method, and at the same time introduces the Hamiltonian diagram determination method and the polynomial function algorithm to make the judgment?"

"Maybe this idea is really feasible."

"It's just that the shadow of this paper seems to be somewhat familiar?"

Staring at the paper in his hand, Tao Zhexuan muttered to himself.

Although it is impossible for him to understand all of this top-level math paper after reading it once, he has turned it over since it was printed, and the paper paper in his hand has been turned up.

What he cares about is not only the solution of the problem of positive integer factorization, but also the shadow of some ideas in this paper, like someone.

If it weren't for the fact that the name of the first author was not that person, and only some of the mathematical ideas were similar, he would even think that the paper in his hand was written by that person.

After flipping through the paper in his hand again, Tao Zhexuan closed his eyes and thought for a while, then picked up the mobile phone on the table and opened the address book.

At the same time, on the other side, Huaguo, in the study of the villa, Xu Chuan was perfecting the idea of solving the weak Riemann conjecture.

At that moment, his phone vibrated on his desk.

Looking up, he glanced at the caller message and answered the phone with some surprise.

"Yo, how did Professor Tao have time to call me?"

Laughing and teasing, Xu Chuan opened his mouth and asked, it was Tao Zhexuan who was far away in the United States who called him.

"You're working on p=np? Guess?"

On the other side, Tao Zexuan didn't care about Xu Chuan's ridicule, and asked directly.

Hearing this, Xu Chuan was slightly stunned, and then reacted that it was probably the senior sister who released the paper in her hand.

Although his name was not signed on the paper, although Liu Jiaxin wanted to put his name on the second work, after all, he provided a lot of help from the beginning of the research to the paper, and even some of the ideas were provided by him.

However, Xu Chuan still refused the request to add a name.

Without it

, he does not lack this glory, but Liu Jiaxin lacks it.

With his name added, the mathematical community, not only the mathematical community, many people may think that it is he who really solves the problem of positive integer factorization, not the senior sister.

But in fact, he knows very well that although he did make some help in it, most of the things were made by Liu Jiaxin himself.

Coming back to his senses, Xu Chuan smiled and said, "No, p=np? Conjecture is not in my field of study."

Hearing this, Tao Zhexuan frowned slightly and asked, "But ...... in that paper?"

Xu Chuan smiled and said, "I helped read the paper, put forward suggestions and defects, and she revised them."

"I see, no wonder." Tao Zhexuan suddenly understood, nodded, and continued, "I thought you made a move."

After a pause, he asked, "You really didn't study p=np?" Puzzle? If so, please let me know!"

Suspicious by Tao Zhexuan, Xu Chuan said with some tears and laughter: "Just a Riemann conjecture is enough to consume all my energy, how can I have time to study p=Np again?" Problem."

On the other side, Tao Zhexuan was stunned for a moment, a little confused.

"Wait..... Wait, you're working on the Riemann hypothesis?"

Quickly coming back to his senses, he eagerly asked, "Has there been progress?" How long will it take? Please be sure to send me your paper as soon as possible!"

Like Drinje, he asked almost without thinking and asked Xu Chuan to send him the paper as soon as possible.

Listening to Tao Zhexuan's request, the corners of Xu Chuan's mouth moved, and he stopped talking.

How come one or two, thinking that he can solve the Riemann conjecture?

He doesn't have that confidence himself, right?

.......