Chapter 237

This cross-university collaborative project was led by six students from three universities.

The teachers in the three schools only played a simple guiding role.

Because it was the first meeting of the research group, all three instructors were present.

But in the next meeting, I am afraid that such a scene will not occur.

Most of the research work on the whole project will be carried out by these six students.

Again, the construction of the research framework for the topic, as well as every detail encountered in the research, is entirely up to the students to decide.

Today, the task of Gu Lu's three instructors is to give some key guidance based on the specific research framework proposed by the students.

The other is that three students are required to choose one of the six students to be the leader of the research group.

The personnel of the leader of this research group are determined by the performance of several people in this meeting.

After Professor Tao announced that everyone would be allowed to speak freely, the atmosphere at the entire conference table was strangely quiet.

Ahem~~

In the end, it was a student at Jinling University who broke the eerie atmosphere.

This Jinling University student's surname is Luo, and his name is Luo Yu.

Luo Yu opened a document in front of him, smiled at everyone, and said, "Then I'll talk about my personal opinion first, which can be regarded as throwing bricks and stones." ”

"The topic we are studying is called 'the problem of the mean of the Fourier coefficient of the divisor function and the self-preserving L-function of the variable quadratic type', as Mr. Tao said before, the topic can be divided into two parts, namely, the problem of the correlation of the variable is a quaternary quadratic and the almost equal problem of the problem, and the problem of the mean of the Fourier coefficient of the self-defended L-function with the variable of the ternary quadratic type. ”

Luo Yu raised two fingers, and then spoke, "For the first part, I have some superficial opinions. ”

"Quadratic forms are very important in the study of number theory. G(m1,m2):=m1^+m2^2, g(m1,m2,m3):=m1^2+m2^2+m3^2, g(m1,m2,m3,m4):=m1^2+m2^2+m3^2+m4^2, this is the basic formula of quadratic type. ”

"In the case of binary quadratic forms, the problem of the mean in relation to the divisor problem has been studied. In terms of ternary quadratic forms, an important problem in number theory is the distribution of prime numbers related to the whole point in the sphere. What we are studying is a question about quaternary quadratic forms. ”

"First of all, what we need to study is that the variable is a quaternary quadratic is a divisor problem and a whole point problem. We can ......."

Luo Yu talked endlessly.

Since everyone has already done their homework, they can completely keep up with the speed of Luo Yu's narration.

The content of Luo Yu's talk is mainly aimed at the first part of the topic, that is, the related problems of quaternary quadratic forms.

For this part, Luo Yu built a fairly complete and detailed project structure framework.

At least in theory, the other five don't hear anything serious.

After that, Luo Yu talked about the second part of the project.

I don't know if it was intentional or if I didn't have time to prepare, but the framework explained was not as perfect as the first part.

After Luo Yu, a student from Jiangsu and Zhejiang University spoke.

Like Luo Yu, the research framework of the first part of the same project is quite perfect, and the research framework of the second part of the project is a bit shoddy, obviously as if it was completed in a hurry.

On Yan University's side, the classmate named Niu Zilin was the third to speak.

To put it simply, in the first part of the project, Luo Yu and Niu Zilin have many similarities in their views and ideas, and the same is true of the project frameworks they have built.

The framework of the subject described by the classmate from Jiangsu and Zhejiang University is a little more cumbersome and complicated than that of Luo Yu and Niu Zilin.

When measured by numbers, that's about a third more work.

In the end, the six of them decided to focus on Luo Yu's framework, and then dismantle the better parts of Niu Zilin's framework to form a new framework.

After more than half an hour of discussion, everyone came up with a final result.

And in this process, Gu Lu, the three teachers, rarely spoke beside them, and more observed the performance of the six people in this process.

After perfecting this framework, Luo Yu turned his head to look at Gu Lu and the three of them, and said politely, "Three teachers, we have completed the discussion of the topic framework for the first part, and I hope you can give us some suggestions for improvement." ”

This is one of the purposes of Gu Lu's participation in this meeting, and naturally they will not refuse.

In fact, in the eyes of the three of them, the six of them have discussed this research framework after such a long time, which is simply full of loopholes.

Teacher Tao and the teacher from Jiangsu and Zhejiang University on the other side looked at Gu Lu with a smile, obviously to give Gu Lu, the host, a chance to perform.

Gu Lu couldn't help laughing, but he didn't refuse.

Gu Lu shrugged his shoulders and said with a smile, "I'll just briefly say a few opinions." ”

Hearing Gu Lu speak, the six students all became serious, pricked up their ears and listened attentively.

"The first point. Gu Lu held up his first finger, "You think too ideally of the progressive formula for solving the quadratic quadratic form. At present, it is quite difficult to directly obtain the asymptotic formula of the quaternary quadratic form using the existing methods. It's not just a matter of method, it's also a question of computation. ”

Therefore, my suggestion is to derive the progressive formula of the quaternary quadratic form by the asymptotic formula of the ternary quadratic cubic hybrid type: (m1^2+m2^2+m3^3,m1^2+m2^2+m3^3+m4^3). ”

Everyone was nodded by Gu Lu's words, and one by one the chicks nodded like pecking rice, and at the same time were surprised that Gu Lu could find their shortcomings so keenly.

"The second point. Gu Lu didn't pause, raised a second finger, and continued, "There is a problem with the determination of the two theorems. ”

"Theorems 1 and 2 are not what you envisioned as only satisfying the 'almost equal' condition and the structure of the quaternary quadratic form, but should also be related to the asymptote. ”

"For example, S(x)=2K1L1x4log x+(K1L2+K2L1)x4+O(x7/2+ε), where K1=2ζ(2)/7ζ(3), K2=4ζ(2)/7ζ(3)(γ+12/7+2ζ(2)/ζ(2)+2ζ(3)/ζ(3)), L1:=∫-∞∞I1(λ)dλ,L2∫-∞∞I2(λ)dλ, I1(λ)=(∫01e(u2,λ)du)4∫04e(- uλ)du,I2(λ)=(∫01e(u2,λ)du)4∫04(-uλ)log udu, then the theorem we construct should be ......"

"The third point, the use of the prime number theorem in the complex plane, is well known......"

Gu Lu didn't stop talking.

"Fourth point ......"

"Point 5......"

……

In more than ten minutes, Gu Lu pointed out more than a dozen deficiencies in the framework of the crowd.

And every problem is real, and there is no Gu Lu who picks bones in eggs.

This result made everyone even more ashamed.

They realized that the almost perfect framework of the subject, which had made them so satisfied, was simply full of loopholes in the eyes of the teacher.

So all of them gathered their pride in their hearts and listened carefully to Gu Lu pointing out their shortcomings one by one.