Scholar’s Advanced Technological System

For Lu Zhou, class with undergraduates is also a review of knowledge points.

If it is normal, these things that are obvious to him are basically not considered. Only at this time can he temporarily put down the study itself and think about what is obvious and why it is obvious.

"... Many people know that Riemann's conjecture is one of the most important and difficult conjectures in analytic number theory. It is a hypothesis about the zero distribution of the Riemann zeta function. But few people know why the Riemann conjecture is. And was it raised?"

"In fact, before the Riemann conjecture, there was a larger proposition that had been studied by non-mathematicians for centuries, that is, the distribution of prime numbers."

Said, Lu Zhou wrote a few numbers on the blackboard, and looked back at the students in the classroom to continue.

"Through the most basic arithmetic theorem, even junior high school students know that each positive integer can be expressed as the product of prime factors. If the order of prime factors is not considered, then this representation is unique, so the prime number becomes The basic elements that make up a positive integer."

"However, the distribution law of prime numbers is not as easy to understand as its definition. It can even be said that one of the most basic tasks of the entire analytic number theory is to study the distribution law of prime numbers."

Looking at the students in the classroom gradually entered the state, Lu Zhou knows that this class has almost been half successful.

Although Riemann’s conjecture is a very complicated issue, it is not as difficult to understand that it is not as much as people think. What is really difficult is how to solve it...

After a pause, Lu Zhou continued.

"In analytic number theory, people usually study the function π(x) and use it to represent the number of prime numbers that do not exceed x. Studying the distribution law of prime numbers is the basic task of analytic number theory, while studying the behavior of π(x) , is the central issue of analytical number theory."

"About the problem of π(x), Gauss and Legendre have done a lot of numerical calculations, and guess that when x tends to infinity, π(x)~x/lnx, this conjecture is later proved, that is, we Understanding the prime number theorem."

“Euclidean proved that there are infinite numbers of prime numbers by using elementary methods, and Euler introduced a product formula. These pioneers provided the possibility to analyze the prime number problem. However, until the 1950s, people did not. Finding the right way to prove Gauss's conjecture, until a German mathematician published a paper entitled "The number of primes that do not exceed a given value" is the study of π(x). Open up a new path."

"Many people may have guessed who this big cow is, yes, he is the Riemann I want to say, and the Riemann zeta function he introduced in this paper has influenced the future for a century and a half. ”

He said that Lu Zhou turned to face the blackboard and wrote a line of calculations on the blackboard.

[ζ(s)=Σ1/n^s]

Looking around at the silent classroom, Lu Zhou continued.

"It's this stuff... it doesn't look too difficult, right?"

All students: "..."

Mmp!

Where is it not difficult? !

“Riemann has further conjectured his own function in the paper, arguing that all non-obvious zeros of ζ(s) are on a critical line. It turns out that his gaze is quite far-sighted and has been obtained through a lot of calculations. All non-obvious zeros are on a critical line. Unfortunately, although we know that it is a good probability, there is no way to prove that it is indeed correct."

“So we can often get a very beautiful result under Riemann's conjecture, but if we can't prove that the Riemann conjecture is true, we can't prove that our results are correct.”

"The reverse is also the same. If we can prove that the Riemann conjecture is correct, then thousands of mathematical conjectures that assume the existence of Riemann's conjecture will be promoted to theorem!"

"If anyone can prove the Riemann conjecture, he will undoubtedly become the greatest mathematician of this century... I can say this sentence very responsibly, even if this century has just begun."

"Professor," at this time, a student couldn't help but raise his hand. After he got a nod from Lu Zhou, he stood up and asked excitedly. "If you can prove the Riemann conjecture, compare it with you?"

"This is not a good comparison. After all, my achievement is not just in the field of mathematics." Looking at the student who asked the question, Lu Zhou smiled and gave an uncertain statement. "But if someone can really prove this conjecture." In that case, his achievements in the field of mathematics will undoubtedly stand at the apex of this era."

Next, Lu Zhou continued to talk about some research progress on the Riemann conjecture, as well as some equivalent forms. Although they are all boring things, perhaps because of the change in the way of teaching, students obviously listen more seriously than the previous one.

I was very satisfied with the fact that I was gradually getting back some status. Lu Zhou nodded in the heart.

The time passed by, and it was soon time for class.

Lu Zhou glanced at the wall clock on the wall. When the time was almost over, he dropped the chalk in his hand on the multimedia desk.

"This class is here, just now I just got some new ideas... Then, class."

In the classroom, the voice of the textbook was smeared. Lu Zhou clamped the lesson under the elbow and nodded to the students who had left him to leave, then turned and walked outside the classroom.

Going outside the classroom, Lu Zhou was preparing to go back to the office and record the inspiration that was produced during the class. Suddenly, he was stopped by the Qin Dean who did not know where to get it.

"A very good number theory class!" With a smile on his face, President Qin said in a sigh of emotion. "Even if I listened to it, I would benefit a lot."

Lu Zhou smiled and said with a smile.

"There is a prize. I haven’t given classes to undergraduates for a while."

Dean Qin said with understanding: "Everything has a sequence, it is related to the national interest. Compared to giving students classes, of course, your research is more important. Speaking, have you been busy recently?"

Lu Zhou: "Is not very busy, what happened?"

"This is the case. I have one thing I want to ask you," Qin said, coughing softly. "You heard about the Olympic Math Competition?"

Lu Zhou: "I heard that I heard that there is any problem?"

He certainly heard of the imo contest, although he did not have the opportunity to participate.

Every year, the gold medal of the imo contest is the same as the fairy.

For example, Schultz, who he knows, is known by Faltins as one of the three most promising young scholars in the world to surpass him. He has won three imo gold medals in a row.

As for being asked to why he took the gold medal and then signed up for two sessions, according to him, it is because he feels fun...

Director Qin smiled and said: "This is the case. Didn't the national high school mathematics league last month? The top names in the provinces have already been selected. To the national finals of the winter camp in January next year, about 30 people will be selected. The students entered the national training team. Now it’s been November, and it’s almost time to prepare questions.”

Lu Zhou squatted slightly, then smiled and said: "... Shouldn't you come to me as a proposition?"

Dean Qin: "This matter is not for me. It is an invitation from the Chinese Mathematical Society. They hope that you will be the protagonist of the final finale."

Lu Zhou: "Let me be a protagonist?"

Director Qin smiled and said: "What is wrong with this. The last question in the national finals in previous years is also the academician's proposition. You are not only an academician, but also a Fields Prize winner. If you are not suitable, then there is still Who can be right?"

Lu Zhou: "That's the way, just the last question."

"Well, I will ask you about this," suddenly thought of something. Qin Dean quickly added another sentence. "Right, don't make it too difficult. If anyone can't do it, it doesn't make sense." It is."

"Reassure, I won't be too difficult," said Lu Zhou, taking a piece of draft paper from the lesson under the elbow, and tearing the corner to write on it.

Looking at Lu Zhou, he took out the draft paper and wrote it. Qin’s dean squatted and then laughed.

"You shouldn't be planning to leave a question here?"

Lu Zhou: "Or not?"

Qin Yuanchang Khan said: "This is the national final. How to say it is a good idea."

"I have already considered it," wrote the question on the paper. Lu Zhou folded the draft paper and gently stuffed it into the hands of Qin Dean. "For me, transfer it to the Chinese Mathematical Society. This topic should not be problem."

Suddenly watching the back of Lu Zhou's departure, Qin Dean moved his eyes to the draft paper in his hand and silently opened his eyes.

"...Riemann zeta function?"

Mouth muttered in the mouth, Qin Dean touched his chin and thought about himself.

"Can such a contest student do it?"

However, at this time, he suddenly seemed to think of something, his eyes were slightly bright.

"Oh... wait, this question seems a bit interesting..."

God mysteriously looked around, Qin Dean carefully put the paper into the pocket, then turned and walked in the direction of the office.