Section 342

Now I even kind of expect Xiao Yi to succeed in advance and then slap this guy in the face!

Of course, considering that this is the Riemann Hypothesis, I won’t let it go, nor will any of us, come on! Xiao Yi, now we know that your paper is your response, so we will do our best to make this challenge more epic! 】

…

"Well...this guy still has a young mentality."

Xiao Yi naturally saw Tao Zhexuan's remarks and couldn't help but sigh.

As of this year, Tao Zhexuan is already 52 years old. He is already an old man, but his mentality has always been young.

Looking back at himself, it may be because as the level of Wuqing Lianxue BUFF gets higher and higher, his mentality becomes more and more rational, which makes him feel more and more like an older person. of people.

"Perhaps sometimes, I should also find some young people's things to do?"

Xiao Yi laughed at himself.

At this time, Wang Hao, who was right next to him, said, "Perhaps you can try to fall in love? Isn't falling in love just what young people do?"

Xiao Yi's brows suddenly raised, he turned to look at Wang Hao, and asked: "If that's not the case for young people falling in love, wouldn't it be called falling in love?"

Wang Hao said with a smile: "If it's not a young man's love affair... I think it's probably a love affair for the sake of carrying on the family line."

Xiao Yi smiled and said: "If I were in love, then I would most likely be in love to carry on the family line. Otherwise, in my current situation, do you think I really have time to enjoy my youth?" What is the experience of falling in love?”

Wang Hao spread his hands and said, "If you want to take time off to fall in love, I think the leaders will agree."

Xiao Yi immediately narrowed his eyes and looked at Wang Hao, and said, "Don't tell me, which leaders have you also received tasks from, to persuade me to get married or something?"

Wang Hao immediately waved his hands and said: "No, absolutely not! I am really just thinking about you."

"What's your relationship with Wang Li?"

Xiao Yi asked again.

"Uh..." Wang Hao couldn't laugh or cry: "Brother Li and I really have nothing to do with each other. As you know, Brother Li's hometown is from Qinxi, and I am from Hui Province."

"Brother Li has been called." Xiao Yi waved his hand directly: "Then don't say anything. Even if you two didn't have a relationship before, you have a relationship now."

Wang Hao shrugged helplessly.

Just kidding, one is Xiao Yi's guard and the other is his assistant. It's hard not to recognize them!

Xiao Yi didn't say any more, lowered his head, looked at the pile of draft paper on his desk again, and continued his research on the Riemann Hypothesis.

But for now, his main research focus is on the development of elliptic inflection analytical methods.

The more he researched, the more he discovered that this method he accidentally created had many possibilities.

Starting from the elliptical angle, it radiates out and gradually covers quite a lot of areas.

Whether it is number theory, algebraic geometry, representation theory, modular forms, or further refinement to various automorphic forms, Dirichlet L-functions, etc., you can find corresponding places.

So much so that the direction he is really exploring now is no longer the Riemann Hypothesis, but the Langlands Programme.

The Langlands Programme, not the Geometric Langlands Programme.

Moreover, what he is involved in now is not the superficial level of Langlands Program, but is directly related to the most important conjecture of Langlands Program, the functority conjecture.

The functority conjecture is an important prerequisite for the realization of the Langlands program, mainly because it has played a huge role in the field of representation theory, number theory and geometry.

In representation theory, it provides a unified framework to understand the relationship between representations of different groups; in number theory, it connects automorphic representations with many important number theory objects, such as L-functions, Galois representations, etc.; In geometry, it inspired many profound thoughts and ideas. For example, the Langlands Program of Geometry was developed thanks to the inspiration brought by the functority conjecture.

Once the functority conjecture can be proven, it will be of great help to the realization of the Langlands Program.

However, judging from the current research status, it is still far away to prove the functority conjecture. Judging from Xiao Yi's current results, what he is most likely to complete is Arting's conjecture.

Artin's conjecture is a typical example of the functority conjecture.

If Artin's conjecture can be proved, it will bring great help to the proof of the functority conjecture.

However, Xiao Yi is now more concerned about proving Arting's conjecture and its role in proving the Riemann conjecture.

Xiao Yi made a simple derivation on the draft paper, and finally was able to easily get a relationship formula.

"Well... to put it simply, in the past, because the classical Riemann hypothesis did not correspond to any kind of Galois representation, even if Atting's hypothesis was proved, it would not play a big role in proving the classical Riemann hypothesis. Help, but it is very helpful to prove the generalized Riemann hypothesis of Artin L-function.”

"But just hearing the name is helpful."

Xiao Yi smiled.

Generalized Riemann hypothesis refers to various generalizations of Riemann hypothesis, and there are many types. Artin L-function Riemann hypothesis is just one of them.

For the most classic Riemann hypothesis, the result of Artin's hypothesis is completely useless.

But now, with the elliptic sigmoidal analysis, even if the classic Riemann hypothesis does not have a corresponding Galois representation, Xiao Yi can make a connection between the two from another elliptic form.

And in this way...

If Artin's hypothesis can be proved, it can bring a huge help to the proof of Riemann hypothesis!

Even, it is equivalent to coming directly to a place that is extremely close to the final proof of Riemann hypothesis.

This is like a shortcut.

Of course, this shortcut is not so easy to take. After all, its premise is to prove Artin's hypothesis first.

And the difficulty of Artin's hypothesis is there after all.

Although Artin's hypothesis is not listed as one of the seven major problems of the millennium, the difficulty of proving it is no less than that of the seven major problems of the millennium.

However, he had solved the Millennium Problem before. Since he dared to come up with such an idea, it means that he had already had the idea to prove Artin's conjecture.

Still the same.

Elliptic anticurve analysis!

Elliptic anticurve analysis has infinite possibilities.

Even on Artin's conjecture, it can also play an extremely huge role!

Xiao Yi's eyebrows slightly raised.

Now, in his mind, there are already a lot of ideas, each of which can become a way of proving Artin's conjecture.

Therefore, for the reply that Liang Qiushi praised him on Bihu, one thing he did not agree with was that elliptic anticurve analysis was not a very ordinary paper among his many papers, but a very important paper.

That is to say, there is still not much research on elliptic anticurve analysis in the mathematical community. If it were not for the paper he published, it would probably take some time for people to really realize that elliptic anticurve analysis has more clever applications.

No more nonsense, then he began to study in depth.

"First, give the Galois representation of the elliptic curve."

"Given an elliptic curve E over the rational number field Q, consider its Tate module T(E), which is the Z-module generated by all-equal points of E. The Galois group Gal(Q/Q) naturally acts on T(E), which gives a Galois representation."

[ρ:Gal(Q/Q)→GL(2,Z)]

"Then we need to use the L function."

Associated with the Galois representation ρ above is the L-function L(s,E) of the elliptic curve E, which can be defined by the Euler product.

[L(s,E)=∏(p) 1/(1-a_p p^(-s)+p^(1-2s)), where p takes all prime numbers (E has good restoration), and a_p is the trace of E on the restoration of the module p]

There are more and more derivations on the draft paper, and the elliptic curve itself can play a very important role in proving the Artin conjecture.

For example, the Taniyama Shimura Theorem can be regarded as the Artin conjecture in the context of ellipse, and the Artin conjecture that Xiao Yi wants to prove now can be regarded as a more general form of the Artin conjecture.

Therefore, the proof process of the Taniyama Shimura Theorem can also be a reference in the process of proving the Artin conjecture.

"Then, using the Langlands correspondence method to study is the best angle."

Xiao Yi raised his eyebrows and chose such an angle from the various ideas that emerged in his mind.

Since it involves the problem of the Langlands program, it must be very appropriate to solve it with the method of the Langlands program.

...

In this way, time passed quietly.

Whether you want to conquer the Riemann hypothesis or the Artin conjecture, it will be destined to be a matter that requires a long time and energy.

This is a long march in mathematics, and there are only a few people, or a dozen people, who can participate in such a long march.

Even some of them will eventually just make up the numbers.

Just like in the past, the only one who can solve a problem is the only one.

…

Chapter 279 How nice it would be if Xiao Yi also joined

2027 passed quietly.

2028 arrived as expected.

According to the economic summary of the year, many foreign countries found that the economic situation this year has slightly declined.

As for China, it is getting more and more prosperous.

The effect of nuclear fusion has shown signs after almost a year, especially the changes in Fei City and several nearby cities. The economic growth rate has even increased by about two times compared with the past, which has made the governments of these regions laugh.

And the more this is the case, the more those regions that are still building nuclear fusion reactors are looking forward to the day when the reactors are officially completed. Of course, this day is coming soon. After all, their nuclear fusion reactors have been built for almost a year. Now most of the reactors have basically been built and have entered the final stage.

It won't be long before nuclear fusion reactors can be truly commercialized on a large scale in China.

At the same time, the JNEO organization has been in a dilemma.