Section 359

At Xiao Yi's current age, there may be a third, fourth, or even more times in the future.

After all, although Xiao Yi has solved almost three of the seven major problems of the millennium, there are still three that have not been solved after removing the Poincaré conjecture.

Maybe Xiao Yi will solve the remaining three problems by then.

However, he is still looking forward to the day when Xiao Yi solves the P=NP problem, because he is also curious about how this problem can be solved.

"But then again, Xiao Yi chose to hold this report today, is it really not intentional?"

Beside him, Fefferman couldn't help but say.

Tao Zhexuan smiled and said, "Maybe it was intentional?"

Why do you say that?

That's because, in a few days, it will be the day of the presidential election.

As a result, he is holding a report meeting on such a day.

"I heard that our respected president has been scolding Xiao Yi in his office these days." Tao Zhexuan also said with a smile.

Anyway, he is happy when the current president is angry.

Feferman also laughed, full of joy.

…

Except for them, the mathematicians sitting in other places were also talking about their own things.

As for the mathematicians who were not invited, they were also discussing whether Xiao Yi's report would be successful, or marveling at the bigwigs sitting in front.

And now these bigwigs have come from afar just to listen to a Chinese report for a few hours, which also makes many Chinese people present feel proud.

At this moment, they are also quite grateful in their hearts that Xiao Yi is their compatriot.

…

Time passed quietly, and finally, it was close to ten o'clock.

"Professor Xiao, there are still three minutes before you go on stage."

The staff came to the lounge and said respectfully to Xiao Yi inside.

"Okay, thank you, I know."

Xiao Yi nodded, then stood up, came to the mirror and took a look at himself.

Well...

He is still young, but compared to his past, he has changed a lot.

Although he has a high IQ, his body is still a human body. With the continuous division of cells, he will eventually grow old.

What will he look like at that time?

He sighed suddenly.

Then he shook his head and returned to his seat, waiting for ten o'clock.

Soon, ten o'clock came.

He stood up, came to the door, and stepped out.

There was no host for this report meeting. He was the host and reporter.

At this time, the conference hall had become quiet, and no one spoke. As the footsteps sounded from the stage, everyone present immediately turned their eyes to the backstage exit.

Soon, the figure familiar to many people present appeared.

Applause suddenly rang out, and many mathematicians in the front row stood up to welcome this mathematical god.

Although it is still to be determined whether his proof is correct or not, it does not prevent them from recognizing him now.

"He is still so young."

Deligne in the audience sighed.

"Yes." Bombieri also nodded.

Finally, Xiao Yi walked to the center of the podium. Facing the many familiar faces present, although he had not seen them for a long time, he smiled and waved.

"Friends, long time no see, I miss you so much."

Everyone present smiled. It was indeed a long time no see.

"Then, please sit down first."

Xiao Yi pressed his hands together, and then the audience sat down one after another.

Then, Xiao Yi said: "First of all, thank you all for coming to my report."

"Today's report will be very long, and I will try to explain to you more comprehensively how I proved the Riemann hypothesis."

"Then, let's not talk nonsense anymore, let's get started."

Xiao Yi turned around and walked to the super long blackboard behind him, and wrote the Riemann hypothesis on it.

"I will not say more about the origin and statement of the Riemann hypothesis."

"All non-trivial zeros of the Riemann zeta function fall on the straight line Re(s)=1/2, which is the goal we want to prove."

"And it represents a goal pursued by us number theorists, that is, to make more accurate predictions about the distribution of prime numbers."

"Of course, many years later, will we be able to find a general formula that can directly generate prime numbers?"

Xiao Yi smiled, then changed the subject and said, "Okay, then let's start with the first step of proving the Riemann hypothesis."

"Elliptic anticurve analysis."

Xiao Yi wrote these words on the blackboard again.

"Elliptic anticurve analysis is one of the most core methods in my entire proof. It provides a lot of help, the most important of which is to help us prove the Artin conjecture and help us give the Riemann hypothesis itself the properties of Galois representation."

"I believe many friends have noticed this while reading my paper."

"Then, let's first give a more comprehensive explanation of the elliptic anticurve analysis method."

Then, Xiao Yi began to write the derivation process of the elliptical recurvature analysis method on the blackboard.

The mathematicians present also watched quietly.

Although their understanding of elliptical recurvature analysis has also reached a relatively in-depth level, they are also very happy to listen to Xiao Yi's more in-depth explanation of this, which may also bring them a lot of inspiration.

And sure enough, as the creator of elliptical recurvature analysis, Xiao Yi showed a lot of detailed thinking that cannot be described in the paper.

"...The most important role of elliptic recurve analysis is to successfully help us connect the Riemann Hypothesis and Galois representation, and the most important step lies in the fourth paper, "CM Elliptic Curves and Hecke Characteristics" "In this article."

"CM elliptic curve is a special type of elliptic curve. We can easily think that their complex multiplication structure brings special properties to their L-function. At this time, we can try By constructing this elliptic curve, an ellipse can be constructed that can be analyzed using elliptic inflection analysis..."

Xiao Yi slowly told and deduced, and finally, he revealed the core ideas in the paper "CM Elliptic Curve and Hecke Characteristics".

The mathematicians present could not help but sigh.

It was Xiao Yi's way of thinking that made them always deeply impressed by him.

"... Specifically, for a CM elliptic curve E, its L-function L(s, E) can be decomposed into the product of two Riemannian Zeta functions."

[L(s, E)=ζ(s) L(s, χ)]

"where χ is a Dirichlet characteristic."

"And this decomposition connects the Riemann Zeta function to the L-function of the elliptic curve."

"Then we can naturally make connections at this time. If we can connect L(s, E) with a certain Galois representation, then through the above decomposition, we will also connect ζ(s) with a certain Galois representation. ”

"In this way, we will achieve a key step."

"Therefore, Hecke's characteristic theory has come into our sight."

"The Hecke characteristic is a basic and powerful tool in modular form theory. Its basic idea is that given a modular form f and a positive integer n modulo N, we define a new modular form Tnf, called n of f Hecke features.”

"For a CM elliptic curve E, we can construct a special Hecke characteristic λ_E that encodes the complex multiplicative structure of E into a Galois representation."

"Specifically, λ_E is a representation from the Galois group Gal(K/K) of a certain number field K to GL_2(C), which satisfies the following properties..."

Along with Xiao Yi's narration, time also passed quietly.

Although what he is describing now is in the fourth paper, in fact, this problem itself should be solved from the beginning, because its most important purpose is to give the Riemann Hypothesis the attribute of Galois representation. In this way, the Artin's hypothesis proved later can be applied to the proof of Riemann's hypothesis.

"Sure enough, you still have to listen to Xiao Yi himself to understand the details."

While listening, Terence Tao sighed with emotion.

Now, he has received a lot of inspiration, and some of the problems that existed in his mind before have been solved at this moment.

This is the point of listening to the report, which allows them to understand the author's own thoughts.

In this way, the first paper and the fourth paper are combined to describe it. Finally, Xiao Yi has basically finished explaining the elliptic recurve analysis.

And time has passed an hour.

Generally speaking, an academic report meeting is about one hour, and at least some rest time should be provided for the scholars present.

But at this time, no scholar is willing to take a break and just wants to continue listening.

"Now, the key points of elliptic recurvature analysis have been explained, but it needs to be noted that in many of the next steps, the influence and role of elliptic recurvature analysis will also exist."

"Then next, we start to discuss the second paper, the discussion of high-dimensional modular curves, which are generalized modular curves."