Chapter 830

For the land boat, having classes with undergraduates is also a review of knowledge points.

As usual, these things are obvious to him, and they will not be considered basically. Only at this time can he put aside his research and think about why the obvious things are obvious.

“…… As many people know, Riemann conjecture is one of the most important and difficult conjectures in analytic number theory. It is a hypothesis about the zero distribution of Riemann zeta function. But few people know why Riemann's conjecture was put forward? "

"In fact, before the Riemann conjecture, there was a larger proposition that has been studied by countless scholars for centuries, that is, the distribution law of prime numbers."

With that, Lu Zhou wrote down some numbers on the blackboard, looked back at the students in the classroom and continued.

"Through the most basic arithmetic theorem, even junior high school students know that every positive integer can be expressed as the product of prime factors. If the order of prime factors is not considered, this representation is unique. Therefore, prime numbers have become the basic prime elements of positive integers."

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

Looking at the students in the classroom gradually into the state, Lu Zhou knew that he had almost half the success of this class.

Riemann conjecture is a very complicated problem, but it is not so difficult to understand it as ordinary people think. The real difficulty is how to solve it

After a pause, the boat continued.

"In the theory of analytic numbers, people usually study the function π (x), and use it to express the number of prime numbers no more than x. The basic task of analytic number theory is to study the distribution of prime numbers, and the central problem of analytic number theory is to study the behavior of π (x). "

"On the problem of π (x), Gauss and Legendre have done a lot of numerical calculation, and conjecture that when x tends to infinity, π (x) ~ x / LNX, this conjecture was later proved, that is, the prime number theorem we know."

"Euclid proved that there are infinitely many prime numbers by elementary methods, while Euler introduced a product formula. These forerunners provided the possibility for the analysis and research of prime number problems. However, until the 1850s, no suitable method was found to prove the conjecture put forward by Goss. Until a German mathematician published a paper entitled" on no more than The paper "the number of prime numbers of a given value" opens a new way for the study of π (x). "

"A lot of people may have guessed who this big bull is. Yes, he is the Riemann I want to talk about, and the Riemann zeta function he introduced in this paper will affect the next century and a half."

He said that the boat turned to the blackboard and wrote a line of calculation on the blackboard.

[ζ (s) = ∑ 1 / N ^ s]

looking around the silent classroom, Lu Zhou continued.

"That's it It doesn't look hard, does it? "

Students: "..."

MMP！

What's not difficult?!

"In this paper, Riemann further conjectured the function he proposed, and thought that all the non obvious zeros of ζ (s) were on the critical line. It turns out that his vision is indeed quite farsighted, and all the non obvious zeros obtained through a lot of calculation are on the critical straight line. Unfortunately, though we know it's probably right, there's no way to prove it's true. "

"Therefore, we can often get a very beautiful result under the Riemann conjecture, but if we can't prove that the Riemann conjecture is true, we can't prove that our result is correct."

"On the other hand, if we can prove that Riemann conjecture is correct, then thousands of mathematical conjectures that assume that Riemann conjecture is true will be promoted to theorems!"

"If anyone can prove Riemann's conjecture, he will undoubtedly become the greatest mathematician of this century I can say it responsibly, even if this century is just beginning. "

"Professor," one of the students raised his hand at this time. After getting the nod of the boat, he stood up and asked excitedly, "if you can prove the Riemann conjecture, how can it compare with you?"

"This is not a good comparison, after all, my achievements are not only in the field of mathematics," Lu Zhou said with a smile, looking at the student who asked, "but if someone can really prove this conjecture, there is no doubt that his achievements in the field of mathematics will stand at the top of this era."

Next, Lu Zhou continues to talk about the research progress of Riemann conjecture and its equivalent forms. Although they are all boring things, perhaps because of the change of teaching methods, the students obviously listen more seriously than the last lesson.

I'm very satisfied with my getting back to some state, and I nodded proudly in my heart.Time passed by minute by second, and soon it was time to finish class.

Lu Zhou took a look at the clock on the wall. Seeing that it was almost time, he left his chalk on the multimedia desk.

"Let's go to this class. Just now I have some new ideas Then, class is over. "

In the classroom, there was a sound of tidying up the textbooks. Lu Zhou put the lesson plan under his elbow, nodded to the students who watched him leave, and then turned to walk outside the classroom.

Walking outside the classroom, Lu zhouzheng is going to go back to the office to record the inspiration he just had in class. Suddenly, President Qin, who doesn't know where to drill out, stops him.

"An excellent number theory class!" With a smile on his face, President Qin said with emotion, "even if I have heard it, I have benefited a lot."

Lu Zhou said with a embarrassed smile.

"I'm flattered. I'm ashamed to say that I haven't taught undergraduate students for a while. "

President Qin said with understanding: "everything has a priority, which is related to national interests. Compared with teaching students, of course, your research is more important. Say, are you busy recently? "

Lu Zhou: "it's not very busy. What's the matter?"

"Well, there's one thing I want to ask you," Qin said with a slight cough. "Have you heard of the Olympic mathematics competition?"

Lu Zhou: "I've heard about it. Is there any problem?"

Of course, he has heard about the IMO competition, although he has never had the chance to participate in it.

Every year, those who get the gold medal of IMO competition are like immortals.

For example, Schultz, whom he knows, is regarded by faltins as one of the most promising young scholars in the world, has won three consecutive IMO gold medals.

As for being asked why he won the gold medal and then went to sign up for two sessions, according to him, it was because he thought it was fun

Qin Yuan said with a smile, "well, didn't he play the national high school mathematics league last month? The first few students from all provinces have been selected. By the national final of winter camp next January, about 30 students will be selected to enter the national training team. It's November now, and it's almost time to prepare for the exam. "

Lu Zhou was slightly stunned, and then he said with a smile: " You didn't come to me to be the proposition person, did you? "

President Qin: "I'm not in charge of this. It's the invitation from the Chinese mathematics society. They hope you will be the last one to finish the test."

Lu Zhou: "is it suitable for me to be a propositional person?"

Qin Yuan said with a smile, "what's wrong with this? The last question of previous national finals is also the academician's proposition. You are not only academician, but also the winner of the fields prize. If you are not suitable, who else can be?"

Lu Zhou: "well, that's the last question."

"Well, it's up to you," President Qin added after thinking of something suddenly. "By the way, don't make it too difficult. If nobody can do it, it's meaningless."

"Don't worry, I won't come out too hard," said Lu Zhou, taking out a piece of sketch paper from the teaching plan under his elbow and tearing off a corner to write on it.

Looking at Lu Zhou taking out the draft paper and writing it, President Qin was slightly stunned, then he couldn't help crying and laughing.

"Are you going to write a question here?"

Lu Zhou: "otherwise?"

"It's a national final, so you have to think about it," said Qin

"I've already thought about it," wrote the question on the paper, and Lu Zhou folded the draft paper and put it into President Qin's hand. "Transfer it to the Chinese Mathematics Society for me. It should be OK on this subject."

Staring at the back of Lu Zhou's departure, President Qin moved his eyes to the draft paper in his hand and opened his eyes in silence.

“…… Riemann zeta function? "

Mumbling a sentence, President Qin touched his chin and thought to himself.

"Can students do this kind of contest?"

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

"Hiss Wait, this question seems to be interesting... "

God secretly looked around, President Qin carefully folded the note into his pocket, then turned around and walked towards the office.