Chapter 830: On-site questions

For Lu Zhou, taking classes with undergraduates can also be regarded as a review of knowledge points.
If it was usual, these things that were obvious to him would basically not be considered. Only at this time can he put aside his research for a while and think about what is obvious.
"... Many people know that the Riemann conjecture is one of the most important and difficult conjectures in analytical number theory. It is a hypothesis about the zero distribution of the Riemann zeta function. But few people know why And was brought up? "
"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."
Speaking, Lu Zhou wrote down a few numbers on the blackboard and 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, then this representation is unique, so prime numbers have become 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 analytical number theory discipline is to study the distribution law of prime numbers."
Watching the students in the classroom gradually enter the state, Lu Zhou knew that he had already completed this lesson almost halfway.
Riemann guessed that although it is a very complicated problem, it is not as difficult as most people think to understand it. 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 primes not exceeding x. Studying the distribution of prime numbers is the basic task of analytic number theory, and studying the behavior of π (x) Is the central issue of analytical number theory. "
"On the problem of π (x), both Gauss and Legendre have done a lot of numerical calculations, and guess that when x tends to infinity, π (x) ~ x / lnx, this conjecture was later proved, which is what we have Understand the prime theorem. "
"Euclidean proved that there are infinitely many prime numbers using elementary methods, and Euler introduced a product formula. These pioneers provided the possibility to analyze and study the problem of prime numbers. However, until the 1850s, people did not Finding a suitable method to prove the conjecture proposed by Gauss, until a German mathematician published a paper entitled "On the Number of Primes No More Than a Given Value", was a study of π (x) Opened a new path. "
"A lot of 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 thesis will affect the future one and a half century. "
Said the landing boat turned to face the blackboard and wrote a line of calculations on the blackboard.
[Ζ (s) = Σ1 / n ^ s]
Looking around the silent classroom, Lu Zhou continued.
"That's the thing ... it doesn't look difficult, does it?"
Students: "..."
mmp!
Isn't it difficult? !!
"Riemann has further conjectured the function he proposed in the thesis and believes that all the non-obvious zeros of ζ (s) are on the critical straight line. It turns out that his vision is indeed quite visionary. All non-obvious zeros are on a critical straight line. Unfortunately, although we know that its high probability is correct, there is no way to prove that it is indeed correct. "
"Therefore, we can often get a very beautiful result under the Riemann conjecture, but if we cannot prove that the Riemann conjecture is true, we cannot prove that our results are correct."
"The reverse is also true. If we can prove that the Riemann conjecture is correct, then thousands of mathematical conjectures that assume the existence of the Riemann conjecture will be promoted to theorems!"
"If anyone can prove the Riemann conjecture, he will undoubtedly become the greatest mathematician of this century ... I can say this very responsibly, even if this century has just begun."
"Professor," at this time, a student couldn't help raising his hand. After getting a nod from Lu Zhou, he stood up and asked in excitement, "If you can prove the Riemann conjecture, how do you compare with you?"
"This is not a good comparison. After all, my achievement is not only in the field of mathematics." Looking at the questioning student, Lu Zhou smiled and gave an uncertain statement, "but if anyone can really prove this conjecture, Then, his achievement in mathematics will undoubtedly stand at the apex of this era. "
Next, Lu Zhou continued to talk about some research progress on the Riemann conjecture, and some equivalent forms. Although they are all boring things, maybe because of the change in the way of teaching, the students obviously listened more seriously than the last lesson.
Satisfied that he gradually recovered some conditions, Lu Zhou nodded proudly in his heart.
Time passed minute by minute, and it was time to end the class soon.
Lu Zhou glanced at the wall clock on the wall and saw that it was almost time, then he threw the chalk on his multimedia desk.
"That's all for this class. Just now I happened to have some new ideas ... well, after class."
The sound of sparsely pulling up textbooks sounded in the classroom. Lu Zhou nodded his lesson plans under his elbow, nodded to the departing students who watched him leave, then turned and walked outside the classroom.
After walking outside the classroom, Lu Zhou was going back to the office to record the inspiration he had just produced during the lesson. Suddenly he was stopped by Dean Qin, who did not know where he came from.
"An excellent class on number theory!" Said Qin, with a smile on his face, and said with emotion, "Even if I have finished listening, I have benefited a lot."
Lu Zhou smiled embarrassedly.
"It's been an award. Ashamed to say that I haven't taught undergraduates for a while."
Dean Qin said understandingly: "Everything has a priority, it is a matter of national interest, and of course your research is more important than teaching students. Speaking of which, have you been busy lately?"
Lu Zhou: "Isn't you busy? What's wrong?"
"That's it. I want to ask you something," Dean Qin said with a cough. "Have you heard of the Olympic Mathematical Competition?"
Lu Zhou: "I've heard of it. Have you heard anything?"
He has certainly heard of the imo contest, although he has not had the opportunity to participate.
Every year, the gold medal of the imo contest is a fairy-like player.
For example, Schultz, whom he knows, is known by Faltins as one of the three young scholars in the world who has the most hope to surpass him. He has won three consecutive imo gold medals.
As for why he was asked to sign up for two sessions after winning the gold medal, according to himself, it was because it was fun ...
Dean Qin said with a smile: "That's it. Didn't you play the National High School Math League last month? The top places in the provinces have been selected. By the January finals of the winter camp next year, about 30 will be selected. Students enter the national training team. It is now November and it is almost time to prepare for the exam. "
Lu Zhou froze slightly, and then laughed: "... Are you asking me to be the proposition person?"
Dean Qin: "I don't care about this. It's our invitation from the Chinese Mathematical Society. They hope that you will be the proposition person for the final question."
Lu Zhou: "Is it appropriate to be a proposition person?"
Dean Qin said with a smile: "What is inappropriate? The last question in the previous national finals was also a proposition of the academician. You are not only an academician, but also a Fields Prize winner ~ EbookFREE.me ~ Not fit, then who else can fit? "
Lu Zhou: "Okay, just the last question."
"Well, I'll leave it to you," Suddenly remembered something, Dean Qin hurried to add another sentence, "Yes, don't make it too difficult, it's meaningless if no one can do it Now. "
"Rest assured, I won't be too difficult," Lu said, pulling out a piece of draft paper from the lesson plan sandwiched under his elbow, tearing a corner and writing on it.
Seeing the landing boat take out the draft paper and write it down, Dean Qin gave a slight stupefaction, and then cried and laughed.
"Aren't you going to ask questions here?"
Lu Zhou: "Otherwise?"
President Qin said, "This is the national final, so you have to consider it carefully."
"I've considered it," wrote the question on the paper, and Lu Zhou folded the draft paper and stuffed it into Dean Qin's hand. "Transfer it to the Huaguo Mathematical Society for me. There should be no problem on this subject. problem."
Staring blankly at the back of Lu Zhou's departure, Dean Qin shifted his gaze to the draft paper in his hand and opened it silently.
"... Riemann's zeta function?"
Muttering in his mouth, Dean Qin touched his chin and thought to himself.
"Can these contestants do it?"
But at this moment, he suddenly seemed to think something, his eyes lightened slightly.
"His ... wait, this question seems a bit interesting ..."
God looked around mysteriously and secretly. Dean Qin carefully folded the notes into his pocket, then turned and walked quickly toward the office.
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