The top student must be diligent.

Chapter 280 Who is Mingya?

The New Year of 2028 has arrived.

Xiao Yi naturally spent the new year at home.

He is not as busy as before. His biggest task at present is to prove the Riemann hypothesis. Even the country has not assigned him any research tasks.

This is mainly because the country also very much expects him to be the first to complete the proof of the Riemann hypothesis.

This event is not only a symbol that can demonstrate the country's scientific level for the United States, but also for China. Especially now, the two competing parties are really mainly these two countries, which makes it even more critical.

In addition, this time Xiao Yi was alone against a group of world-leading mathematicians. Although the Prime Number Pioneer Project was mainly initiated by Princeton University, it brought together mathematicians from all over the world, of course, most of them were from Europe and the United States.

Under such circumstances, if Xiao Yi succeeds in winning, it would be something worth publicizing.

Therefore, the country has given Xiao Yi enough time to allow him to devote all his energy to the study of this issue.

Of course, unlike the United States, where the president personally went to Princeton University to meet with the mathematicians of the Prime Number Pioneer Project and expressed his earnest hopes for them on this matter, China did not specifically look for Xiao Yi for this matter. At most, Director Liu talked about this matter when he happened to chat with Xiao Yi before, and then simply expressed his blessings to Xiao Yi, and then did not say anything else, which meant that Xiao Yi was allowed to play freely on this matter.

Of course, it would be best if we could win.

……

"I heard that you've been studying the Riemann hypothesis recently, right? It seems to have attracted international attention?"

At the New Year's Eve dinner, Xiao's father happened to mention this matter to Xiao Yi.

Xiao's mother also nodded: "Yes, I saw it on the news. Even the President of the United States mentioned you specifically."

In the past, they would never have imagined that their son would be specifically mentioned by the President of the United States and that the president would say that he would be dealt with specifically.

It's just like a little cow riding on an airplane, so cool.

Xiao Yi spread his hands and said, "It's nothing. It's just a famous conjecture in mathematics. They want to prove that the United States is still very powerful by defeating me."

Mother Xiao said with a smile: "Our son is really amazing!"

Father Xiao rolled his eyes and said to his wife, "Don't listen to this kid's nonsense. He is just bragging about himself."

Xiao Yi shrugged.

Well, if you don’t believe it, forget it.

To be honest, what he said was conservative.

Without further ado, he continued to eat.

The sumptuousness of the New Year’s Eve dinner made him feel like he could eat several bowls of rice in a row.

But after eating for a while, Father Xiao said, "It's 2028 now, you're 25 years old, right? When are you going to find a partner?"

Mother Xiao also remembered it at this time, and said, "Oh, right, now that your zodiac year has passed, it's good to get married this year. But I heard from Xiao Wang that you have a good relationship with a female professor in your Science Island Laboratory. Is that true?"

Xiao Yi almost spit out a mouthful of rice.

He widened his eyes and said, "Wang Li actually told you something like this?"

"That's what I asked." Xiao's mother said, "Don't blame Xiao Wang."

"A female professor is fine." Father Xiao nodded: "At least she's a good match for you."

At this time, Xiao's mother said again: "But you have to be careful to distinguish. You are a celebrity now. Those women who want to approach you deliberately probably want to get close to you. Don't be deceived by such women. The most important thing is to find a good girl."

Father Xiao also nodded and said, "Yes, your mother's words make sense. Be careful to distinguish them, and don't find someone who wants to drive away the parents-in-law when they move in."

Xiao Yi didn't know whether to laugh or cry, and said, "You two don't take my intelligence seriously enough. My eyes are my ruler."

"not to mention……"

I thought about Luo Mingya's usual behavior and it was completely different from what they said. Of course, the most important thing was that Luo Mingya's family was also extraordinary.

So he said, "That female professor is not at all like what you guys are saying now. She is actually quite caring."

Xiao's father and mother immediately showed a half-smile expression, "Oh~~"

Looking at the expressions of the two, Xiao Yi curled his lips and asked, "What's wrong with your expressions?"

Xiao's mother said with a smile: "So now you admit that there is such a female teacher?"

Father Xiao also said with a smile: "And now they are starting to talk to others."

Xiao Yi held his forehead with his hand.

Father Xiao reached out and patted his shoulder, saying, "So, although your IQ is indeed very high, your mother and I can still catch you together."

Xiao Yi spread his hands.

Then he said, "Okay, the two of you don't need to worry so much. Everything depends on fate. Don't you see how high the divorce rate is among young people nowadays? There are many who get married in their thirties or even never get married. There is no need to rush."

Father Xiao said, "Your mother wants to have a grandson. You should try harder. You can't let your mother and I do it, right?"

Xiao's mother rolled her eyes at him and said, "What are you saying in front of the child?"

Xiao Yi shrugged.

……

The New Year’s Eve dinner, which only happens once a year but seems so ordinary, ended just like that.

For Xiao Yi, such conversations now happen frequently.

But as I said, it is never easy to make a decision when it comes to love.

Now he would rather focus all his energy on the research of Riemann hypothesis.

As for how long it will take to solve the Riemann hypothesis, he himself is not very clear. After all, he is still trying to prove the Artin conjecture.

Although several months have passed and he has made a lot of progress in proving Artin's conjecture, he is still a long way from completing the proof.

Artin guessed that it was not a simple question after all.

As a typical example of the functor conjecture involved in the Langlands program, its current significance is not only for the Riemann hypothesis, but also for the functor conjecture.

And just like that, a few days passed.

It was not until the sixth day of the New Year that Xiao Yi suddenly heard his mother say that she had invited the old lady next door and her daughter to come over and have dinner together.

Xiao Yi was stunned. What the hell was that?

Why do you suddenly want to invite others to your house?

Then Xiao's mother said that since the neighbor lady's daughter was a professor at the University of Science and Technology like him, it would be good for them to communicate more.

What's more, when he was not at home, she and the old lady would often chat together, and they would often go out to exercise together in the morning.

Inviting someone to visit is just a very normal interpersonal interaction.

Xiao Yi was helpless. He always felt that they would talk about something they shouldn't talk about.

……

Around three o'clock in the afternoon, the old lady next door came to visit, and of course Sun Lina came too.

"Happy New Year, Professor Xiao." Sun Lina greeted Xiao Yi with a smile.

"Happy New Year, Professor Sun." Xiao Yi nodded.

The old lady also looked at Xiao Yi with a smile, and she looked at him from head to toe.

Finally, he said, "Professor Xiao, every time I think about a great scientist like you living next door, I feel happy."

"But don't worry, I've never told anyone about this, so you don't have to worry about being discovered."

"Thank you, grandma." Xiao Yi said.

Sun Lina's eyes widened as she corrected him, "Professor Xiao, you should call my mom auntie. Otherwise, wouldn't I be a generation older than you?"

Xiao Yi suddenly realized that he didn't want to be younger than Sun Lina for no reason, so he corrected himself and called her "Auntie."

The old lady laughed and said, "You really should call me auntie. After all, Mingya is also my niece."

Xiao Yi broke out in a cold sweat. As expected, his mother beside him asked curiously, "Sister, who is Mingya you are talking about?"

The old lady smiled and said, "Didn't your son tell you?"

"No way." Xiao's mother shook her head: "I can't even hear a girl's name from his mouth."

The old lady laughed and said, "Mingya is my niece. She is currently working as a researcher in Professor Xiao's Science Island Laboratory..."

bad!
Xiao Yi no longer had the heart to continue listening to what they were talking about next.

Although I had anticipated something bad happening, I didn't expect it to happen so soon.

He caught a glimpse of Sun Lina's expression of watching the show, and he just said: "I'm going back to my room."

Then he left the living room directly.

I returned to my room, locked the door, and sat down at the desk.

At this moment, only mathematics could divert his attention.

"Um……"

"What I need to do now is to establish this 'extended L function'. The L functions that I established several times before all seem to be slightly unable to meet my requirements..."

Xiao Yi thought about it for a moment.

"The conditions that this extended L function needs to satisfy are... not only depending on E itself, but also on some additional geometric data on E, such as some special cycle classes on E."

"Well……"

Xiao Yi frowned as he thought, but suddenly he remembered what Luo Mingya once said, don't frown when thinking, otherwise it will be easy to get wrinkles in the future.

So he relaxed his brows again and continued thinking.

"In traditional theory, for an elliptic curve E, we usually consider its Hasse-Weil L-function, defined as..."

[L(s, E)=∏(p) 1/(1-a_p p^(-s)+ p^(1-2s))】

"where p is every prime number and a_p is the trace of E in the reduction modulo p."

"It's just that this L-function doesn't fully capture all the arithmetic properties of E, especially some special geometric structures, which are the ones I need."

"The loop class must be included..."

"Well……"

Xiao Yi closed his eyes.

Perhaps the relaxation of his brows brought about some changes, and he suddenly had some ideas.

"For each prime number, if we consider the p-adic etale cohomology group H^i(E, Q^p)(i=0) of E..."

"Well, these cohomology groups can carry a lot of geometric information about E. In addition, H^1(E, Q^p) also contains the Tate module T^p(E) of E as a subspace."

Xiao Yi's eyes suddenly lit up, and the problem he was facing suddenly had a solution.

Then he began to deduce on the draft paper, mainly using the p-adic etale cohomology group.

As for the p-adic etale cohomology group, he knew it very well.

After all, the self-conservation theory of Etale algebraic varieties that he first developed was based on this theory. Until now, the self-conservation theory of Etale algebraic varieties is still a popular theory in the mathematics community. As for his original paper, it has been cited more than 200 times.

For other disciplines, more than 200 citations may be considered a lot, but not a particularly large number.

But for mathematics, more than 200 citations are definitely quite a lot. Even a classic paper from decades ago may only have 100 or 200 citations to date.

This is because the threshold for mathematics is too high, and these classic mathematics papers are bound to be quite abstract. There may not be many people who can understand them later, let alone write a paper that can use this theory.

The reason why Xiao Yi's paper has been cited more than 200 times in less than ten years is that it is relatively easy to understand and can be used in many places. When his paper was first published, it caused a lot of discussion in the mathematics community, and many people's problems were solved because of the self-protection theory of Etale algebraic varieties.

That’s why it has such a high number of citations.

"So... now define the extended L-function of E as..."

[L(s,E,)=∏(p) 1/det(1-Frob_p p^(-s)| H^1(E,Q)_sp)】

Finally, the new L-function was successfully established and Xiao Yi began to analyze it.

Soon, his eyes lit up.

"Yes, this new L-function can also be extended to the entire complex plane."

Of course, at this time there is no need to continue to use the elliptic inverse analysis method to analyze and extend this thing.

Xiao Yi directly used the most traditional analytical extension method and successfully completed the analytical extension of this L-function.

Then, we start to observe this extended L-function.

Undoubtedly, this new L-function satisfies some special functional equations.

However, when Xiao Yi saw it for the first time, the first thing he observed was that this new L-function is closely related to the Weil conjecture of the elliptic curve E.

“Seems feasible?”

He narrowed his eyes slightly and did a simple deduction in his mind.

However, when approaching the Weil conjecture, some technical obstacles were encountered.

"It's a technical obstacle. This will take some time."

Technical obstacles in mathematics are like a complex set of math problems that require a combination of various methods to solve.

However, this does not seem to be so difficult for Xiao Yi.

However, just as he was about to take the next step, there was a knock on the door of the room.

"It's time for dinner." Mom's voice rang out.

Xiao Yi's helpless voice followed.

"Know it!"

(End of this chapter)