The New Year of 2028 has arrived.
In the new year, Xiao Yi naturally spent it at home.
Now he is not as busy as before. His biggest task at the moment is to prove Riemann Hypothesis. Even the country has not arranged any research tasks for him.
This is mainly because the country also looks forward to him being the first to complete the proof of Riemann Hypothesis.
This matter is not only a symbol that can highlight the country's scientific level for the United States, but also for China. Especially now, the two competing parties are really mainly their two countries, which is even more critical.
In addition, this time it was Xiao Yi who faced off against a group of the world's top mathematicians. Although Prime Pioneer Program was mainly led by Princeton University, it brought together mathematicians from all over the world. Of course, most of them were European and American mathematicians.
Under such circumstances, if Xiao Yi succeeds in winning, it will be something worthy of publicity.
Therefore, the state has left enough time for Xiao Yi to devote all his energy to the research of this issue.
Of course, unlike the United States, where the president personally went to Princeton University to meet with those Prime Pioneer Program mathematicians, and expressed his ardent hopes for them specifically on this matter, China has not specifically approached Xiao Yi about this matter, and at most it is Director Liu When accidentally chatted with Xiao Yi before, he talked about this matter, and then simply expressed his blessings to Xiao Yi, and then did not say anything else. It can be regarded as allowing Xiao Yi to express himself freely on this matter.
Of course, it would be best if we can win.
"I heard that you are currently studying that Riemann Hypothesis, right? It seems to have attracted international attention?"
At the New Year's Eve dinner, Father Xiao accidentally mentioned this matter to Xiao Yi.
Mother Xiao also nodded. "Yes, I saw it on the news, and even the President of the United States specifically mentioned you."
In the past, they would never have imagined that their son would be specifically mentioned by the President of the United States and that he would be dealt with specifically.
It's like a heifer flying on a plane, and NB going to the sky.
Xiao Yi spread his hands and said, "It's nothing, it's just a well-known conjecture in mathematics, and then they want to prove that the United States is still very powerful by defeating me."
Mother Xiao said with a smile, "Our son is so awesome!"
Father Xiao rolled his eyes and said to his wife, "Don't listen to this kid's nonsense. He is bragging about himself."
Xiao Yi shrugged his shoulders.
Yes, if you don't believe it, I will pull you down.
To be honest, what he said was an understatement.
Without further words, he continued eating.
The New Year's Eve dinner was so rich that he felt like he could eat several bowls of rice in a row.
But after eating for a while, Father Xiao said again, "It's 2028 now. Are you 25 years old? When are you going to find a partner?"
Mother Xiao also thought of it at this time, and said, "Yes, now that the birth year has passed, it is good to get married this year, but I heard from Xiao Wang that you have a very good relationship with your Science Island Laboratory female professor? Is it true?"
Xiao Yi almost spit out a mouthful of rice.
He widened his eyes and said, "Wang Li, that guy actually told you such a thing?"
"This is what I asked." Mother Xiao said, "Don't blame Xiao Wang."
"Female professor, too." Father Xiao nodded. "At least I'm a good match for you."
Mother Xiao added at this time, "However, you should also pay attention to the distinction. You are also a celebrity now. Those women who want to get close to you on purpose are probably with the intention of getting close to you. Don't be fooled by that kind of woman. The most important thing is to find a good girl."
Father Xiao also nodded and said, "Yes, what your mother said makes sense. Pay attention to your discernment and don't find someone who wants to drive away your parents-in-law when you move in."
Xiao Yi didn't know whether to laugh or cry, and said, "You two don't take my IQ seriously enough. My eyes are rulers."
"What's more..."
I thought about Luo Mingya's usual behavior, which was completely different from what they said. Of course, the most important thing is that Luo Mingya's family is not ordinary either.
So he said, "That female professor is not like what you are talking about now. She is quite good at taking care of others."
Father Xiao Mother Xiao immediately showed a half-smiling expression, "Oh~~"
Looking at the expressions of the two of them, Xiao Yi twitched his lips and asked, "What's the matter with your expressions?"
Mother Xiao said with a smile, "So now you admit that there is such a female teacher?"
Father Xiao also said with a smile, "And now I have started to talk to others."
Xiao Yi supports the amount.
Father Xiao reached out and patted him on the shoulder and said, "So, although your IQ is indeed very high, your mother and I can still get you in trouble."
Xiao Yi spread his hands.
Then he said, "Okay, you two, don't worry so much. Everything has to be about fate. Don't you look at how high the divorce rate among young people is now. There are many people who get married in their thirties or even never get married. We are not in a hurry."
Father Xiao said, "Your mother wants to have a grandson. You'd better work hard. You can't let your mother and I work hard, right?"
Mother Xiao rolled his eyes at him and said, "What are you talking about in front of the children?"
Xiao Yi shrugged.
The New Year's Eve dinner, which happens once a year but seems to be extremely daily, ended like this.
For Xiao Yi, such conversations happen quite often now.
But again, emotional matters are never so easy to make decisions.
Now, he is still willing to put all his energy into the research of Riemann Hypothesis.
As for how long it will take for Riemann Hypothesis to be solved, he himself is not very clear. After all, he is still trying to prove Artin Conjecture.
Although several months have passed now, and he has achieved a lot of results in the proof of Artin Conjecture, he is still far away from the actual completion of the proof.
Artin Conjecture, after all, it is not a simple question.
As a typical example of the functority conjecture involved in Langlands Program, its current significance is not only for Riemann Hypothesis, but also for the functority conjecture.
In this way, a few days passed.
Until around the sixth day of the lunar month, Xiao Yi suddenly heard from his mother that he invited the old lady next door and her daughter to come over as guests and they would have dinner together.
Xiao Yi was suddenly confused, what is this?
Why do you suddenly want to invite others to your home again?
Then Mother Xiao said that anyway, the neighbor's old lady's daughter was USTC's professor just like him, so it would be good to have more exchanges with her.
What's more, she and the old lady often chat together when he is not at home, and they often go out to exercise together in the morning.
Inviting others to be guests can only be regarded as a very normal interpersonal interaction.
Xiao Yi Helpless, he always felt that they would talk about something they shouldn't talk about again.
Around three generations in the afternoon, the old lady next door came to the door, and of course Sun Lina.
"Happy New Year, Professor Xiao."
Sun Lina smiled and greeted Xiao Yi.
"Professor Sun Happy New Year." Xiao Yi nodded.
The old lady also looked at Xiao Yi with a smile, and she looked at it from beginning to end.
Finally, he said, "Professor Xiao, I really feel happy every time I think about a great scientist like you living next door."
"But don't worry, I have never mentioned it to anyone, so you don't have to worry about being discovered by others."
"Thank you grandma then." Xiao Yi said.
Sun Lina next to him widened his eyes and corrected. "Professor Xiao, you should call my mother aunt, otherwise, wouldn't I be a generation older than you?"
Xiao Yi suddenly realized that he didn't want to be a generation younger than Sun Lina for no reason, so he corrected his name: "Auntie."
The old lady laughed and said, "You should really call me aunt. After all, Mingya is also my niece."
Xiao Yi broke out in a cold sweat. Sure enough, the mother next to her asked curiously, "Sister, who is Mingya you talking about?"
The old lady smiled and said, "Didn't your son tell you?"
"No way." Mother Xiao shook his head. "I can't even hear a girl's name from his mouth."
The old lady laughed and said, "Mingya is my niece, and she is currently working as a researcher at Professor Xiao's Science Island Laboratory..."
Bad!
Xiao Yi has no intention to continue listening to what they are talking about next.
Although I had expected something bad to happen before, I didn't expect it to happen so soon.
Out of the corner of his eye, he caught a glimpse of Sun Lina's expression as he watched the show. He simply left a sentence: "I'm going back to my room."
Then he left the living room directly.
I returned to my room, locked the door, and sat in front of my desk.
At this moment, only mathematics could divert his attention.
"Well..."
"What I have to do now is to build this 'extended L-function'. The L-function I built several times before seems to be slightly unable to meet my requirements..."
Xiao Yi thought for a moment.
"The conditions that extended L-function needs to meet are... not only dependent on E itself, but also on some additional geometric data on E, such as some special cycle classes on E."
"Well..."
Xiao Yi frowned and thought, but suddenly remembered that Luo Mingya once said, don't frown when thinking, otherwise you will easily get wrinkles in the future.
So he frowned again and continued to think.
"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 takes all the prime numbers, a_p is the trace of E on the reduction modulo p."
"It's just that this L-function does not fully capture all the arithmetic properties of E, especially some special geometric structures, which are the structures I need."
"The loop class must be included..."
"Well..."
Xiao Yi Close your eyes.
Perhaps the stretching of his brows brought about some changes and suddenly gave him some ideas.
"For each prime number, if we consider the p-adic etale cohomology group H^i(E, Q^p)(i=0, 1, 2) 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. The problem he was encountering now suddenly had a solution.
Then he began to deduce on the scratch paper, mainly using the p-adic etale cohomology group.
As for the p-adic etale cohomology group, he knows it very well.
After all, his earliest automorphic theory of etale algebraic varieties was based on this theory, and until now, the automorphic theory of etale algebraic varieties is still a popular theory in the mathematics world. As for his original paper, it has been cited more than two hundred times.
For other disciplines, more than two hundred citations may be considered a lot, but it is not particularly large.
But for mathematics, more than two hundred citations are definitely quite a lot in mathematics. Even a classic paper from decades ago may only have one or two hundred citations now.
This is because the threshold for mathematics is too high, and these classic mathematics papers must be quite abstract. There may not be many people who can understand them in the future, let alone write a paper that can use this theory.
Xiao Yi's paper has been cited more than 200 times in less than ten years, mainly because his paper is relatively easy to understand and can be used in many places. When his paper was first published, it caused a discussion in the mathematics community. Many people's problems were solved due to the automorphic 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 establishment of this new L-function was successfully completed, and Xiao Yi began to analyze this new L-function.
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 Analytic Continuation method to analyze and extend this thing.
Xiao Yi directly used the most traditional analytic continuation method to successfully complete the analytic continuation of this L-function.
Then, start observing this extended L-function.
Undoubtedly, this new L-function satisfies some special functional equations.
However, the first thing Xiao Yi observed at first glance was that this new L-function is closely related to Weil Conjecture of the elliptic curve E.
"Seems feasible?"
He narrowed his eyes slightly and simply deduced it in his mind.
However, when moving closer to Weil Conjecture, we encountered some technical obstacles.
"There are technical obstacles. This will take a while."
Technical obstacles in mathematics are like a collection of mathematical problems that require a combination of methods to solve.
However, this does not seem to be that 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 to eat." Mom's voice rang.
Xiao Yi's helpless voice sounded.
"I know!"