The top student must be diligent.

Chapter 97: Ivanets, the Master of Sieve
Liu Dongchen took out his mobile phone, opened WeChat, and entered a group.

Chen Beihua took a look and found that the group was called [The Hope of Chinese Number Theory].

He curled his lips and asked, "What kind of group name is this?"
However, he could probably guess that the people in this group were probably all Chinese mathematicians who specialized in number theory.

Ok……

Because he also joined a group called [Fanfunctoral Light Kingdom].

Liu Dongchen turned on the camera, took a picture of the computer screen, and then sent it to the group.

【image】

[Brothers, and masters, look at what is written here. I feel that it may be something for the classification and research of the parity problem of the sieve method. Let some people who understand it talk about it. ]

However, probably because the picture he took directly from the computer screen was covered with moiré patterns, the group members started to complain about it using emoticons.

【（Did you take the photo holding the door lock.jpg）】

[(The screenshot key given to you by God, the screenshot key given to you by Hua Teng, the screenshot key given to you by Gates, and the sb who still hasn’t learned how to take a screenshot.jpg)]

【…】

Looking at these messages, Liu Dongchen curled his lips. How come these idiots have all kinds of emoticons?

Then he typed back: [Fuck, is this the point? Look at the picture! You will be scared to death after seeing it! ]

Finally, people in the group returned to normal.

[Hey, isn't this Xiao Shen? What video is this? Send it to me and let me see it]

[Don't talk, I'm thinking]

Liu Dongchen logged into Bilibili on his mobile phone, found the video, and sent it to the group.

After a while, a big shot finally showed up.

Tao Quan: [These few lines are amazing. I just took a quick look at them. What Dongchen said is indeed good. It is indeed a classification specifically for the parity problem. However, for now, I can only see that it is a classification for all even prime factors. The odd prime factors are not mentioned. Is there anything else to come? ]

[Oh my god, Professor Tao! ]

【Professor Tao appears! 】

Tao Quan is a mathematics professor at Danfu University. His major research area is number theory. He is very knowledgeable about prime number problems and Diophantine equations. He can be considered a big shot in their group.

Liu Dongchen never expected that a picture he posted could actually attract such a big shot. He looked at the screen and saw that Xiao Yi had written two more lines of formulas, but there was nothing below.

So he took the photo again and sent it out.

【Xiao Yi only wrote these two lines afterwards, and then nothing more.】

Soon, Tao Quan replied again: [That's right! Adding these two lines will also include the odd prime factor class. This is a very feasible idea! It may greatly optimize the obstacle of the sieve method in the parity problem. The only problem is that it is a bit difficult to do it later. First of all, we have to find a way to prove that this classification method can really distinguish the two types of integers. In addition, we must also face the thin sequence problem. We all know that it is difficult to show the infinity of prime numbers in a given thin integer sequence, and so far there is no polynomial that can achieve this.

Of course, the most critical thing is that there are still some technical difficulties. If we cannot overcome these problems technically, everything will be in vain. 】

Tao Quan is indeed an expert in this field. He quickly figured out the information revealed in these few lines of formula.

【Professor Tao is awesome! 】

People in the group started to swipe.

However, Tao Quan sent another message at this time: [However, do you think the person in the video is Xiao Yi? ]

Liu Dongchen quickly replied: [Yes.]

Tao Quan: [I was wondering why he looked so young. If it was Xiao Yi, then it’s understandable.]

[However, why did Xiao Yi suddenly start studying the sieve method? The self-conservation theory of etale algebraic varieties that he worked out some time ago has little to do with the sieve method. ]

As soon as Tao Quan's message came out, the people in this group immediately started thinking.

Yes, why did Xiao Yi suddenly start studying the sieving method?

What problem is he targeting now?

Someone in the group posted a message: [Is it the twin prime conjecture? ]

[Wo Ri, no way? ]

[He just proved the Elliott-Halberstam conjecture, and now he plans to prove the twin prime conjecture? Is this too exaggerated?]

[Maybe the proof of the Elliott-Halberstam conjecture was intended for the twin prime conjecture?
[After all, the proof of the Elliott-Halberstam conjecture directly pushed the twin prime conjecture to 6. From this perspective, Xiao Shen has also solved the question of whether there are infinite pairs of individual primes.]

[Impossible, absolutely impossible! 】

【…】

Various speculations also made the members of this group excited.

Until the end, Professor Tao Quan stood up again and stopped them from spreading the information.

If this turns into a rumor, wouldn't it affect Xiao Yi himself?
[Okay, I think you guys should stop guessing. Even if this is true, the twin prime conjecture is not that easy to solve. However, if Xiao Yi really solves this problem, then I would like to call him the real hope of our Chinese number theory! ]

……

Putting down the phone, Liu Dongchen let out a breath, and his slightly restless heart calmed down a little. "How is it?"

Chen Beihua next to him asked.

"Hmm...what do you want to hear? About these lines or about my idol."

Chen Beihua curled his lips and said, "Don't talk about idols anymore."

But he was still curious: "What happened to Xiao Yi?"

"Have some respect. How can you address God Xiao by his name?"

Liu Dongchen corrected Chen Beihua's address with a serious look, then he clasped his fists and bowed in the direction of Feishi, saying solemnly: "God Xiao, you are now solving the twin prime conjecture for the entire number theory community!"

Chen Beihua, who was about to slap this brainless fan, was suddenly shocked, with a look of disbelief on his face.

"Walter?"

Twin prime conjecture?

Damn it, if Xiao Yi really proves this conjecture, then there's nothing wrong with him becoming a die-hard fan of Xiao Yi!

……

Just like that, this video, which was originally just a video of Xiao Yi solving a difficult problem, began to spread in the professional mathematics circle because of the few lines of formulas he wrote in the process.

For example, Professor Tao Quan also communicated with some mathematician friends he was familiar with.

Eventually, this video was also spread abroad.

……

Rutgers University, New Jersey, USA.

Rutgers University is the eighth oldest institution of higher education in the United States and the second oldest university in the state of New Jersey. The oldest university is Princeton University.

At this time, a number theory class was being held in a classroom in the Department of Mathematics at Rutgers University.

The lecturer was an old professor who looked to be in his seventies.

"In the past, mathematics expected that any irreducible polynomial with integer coefficients would have infinitely many prime values, provided that it satisfied some obvious local conditions."

"It can also be expected that the frequencies of these prime numbers obey a simple asymptotic law."

"However, these asymptotic laws have been shown to apply only to a few special polynomials, and not to all of them, so this is quite unfortunate."

"To give a simple example, a prime number in the form of x^2+y^4."

"However, as I just explained, these are things of the past, and now these problems have been resolved to a certain extent."

"That is the sieving method. In this class, I will start with the sieving method."

……

The classroom was very quiet. Apart from the old professor's voice, there was almost no other sound. The students were listening to the old professor's lecture very seriously.

As for the students' seats, they were almost all occupied, and even the aisles were almost full of people.

There is no other reason, because the old professor's name is Henryk Ivanets.

Master of sieve theory, expert in analytic number theory.

He and another mathematician named Friedlander once proved that there are infinite prime numbers of the form a^2+b^4. Before that, the mathematical community generally believed that this result was out of reach.

The reason they were able to prove this problem was that they achieved further optimization of the screening method, thus overcoming previous difficulties and completing this heavyweight achievement.

Later, Zhang Yitang's breakthrough in the twin prime conjecture was also closely related to the sieve method optimized by Ivanets and others.

The fact that such a top-notch mathematician came to teach number theory, and even talked about the sieve method, naturally attracted many students to attend.

Perhaps among so many students, there are some who have come from Princeton University to attend the class.

Time passed slowly. Ivanets spoke slowly but in detail. At least, every student in the audience could understand him.

At the end of the class, Ivanets said with a smile, "Okay, that's all I have to say for this class. Now, if you have any questions, you can ask me."

Soon, many students raised their hands, and Ivanets began to call on their names and answer their questions.

This continued until the fifth student asked a question.

"Professor Ivanets, I recently saw a video on the Internet, and some of the content in it is about the sieve method. Some people say that the content above may provide some help in solving the parity problem in sieve theory, that is, the parity problem you just mentioned. Can I write it out for you to see?"

“Oh?” Ivanets smiled and said, “I’m glad that some students can understand things related to sieve theory before class. Of course, you can go up and write these things down.”

"Okay!" The student nodded excitedly, then quickly walked to the blackboard, took out a piece of copied paper, and started writing on the blackboard.

【A(x)A(√x)(log x)^2】

[∑_(d≤y)μ^2(d)g(d)=c1·log y+c0+O((log y)^-8)】

……

(End of this chapter)