Chapter 237

This cross-school cooperation project is led by six students from three universities.

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

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

But I’m afraid this kind of scene won’t happen in subsequent meetings.

Most of the research work on the entire topic will be carried out by these six students.

Similarly, the construction of the research framework for this topic, as well as every detail encountered during the research, were all decided by this group of students.

The tasks of the three instructors Gu Lu today are, first, to provide some key guidance based on the specific research framework proposed by the students.

The other one requires three people to choose one of the six students to be the leader of the research group.

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

After Professor Tao announced that everyone could speak freely, the atmosphere at the entire conference table became strangely quiet.

Ahem~~

Finally, it was a student from Jinling University who broke the weird atmosphere.

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

Classmate Luo Yu opened a document in front of him, smiled at everyone, and said, "Then let me share my personal views first, which can be considered as an introduction to the topic."

"The topic we are studying is called 'the problem of the mean Fourier coefficients of divisor functions and automorphic l functions whose variables are quadratic'. As Teacher Tao said before, this topic can be divided into two parts, namely variables

are related problems of the quaternary quadratic form and the almost equivalent problem of this problem, as well as the problem of the mean Fourier coefficients of the automorphic l-function whose variables are the ternary quadratic form."

Student Luo Yu raised two fingers and then said, "For the first part, I have some simple opinions."

"Quadratic forms are very important in the study of number theory. g(m1,m2):=m1^m2^2, g(m1,m2,m3):=m1^2m2^2m3^2, g(m1,m2,m3

,m4):=m1^2m2^2m3^2m4^2, this is the basic formula of the quadratic form."

"In terms of binary quadratic forms, someone has studied the mean problem related to the divisor problem. In terms of ternary quadratic forms, an important issue in number theory is the distribution of prime numbers related to integers in the sphere. What we study,

It’s a related question about quaternary quadratic forms.”

"First of all, what we need to study is that the variable is a quaternary quadratic type, which is a divisor problem and an integer problem. We can..."

Classmate Luo Yu spoke eloquently.

Since everyone has done their homework a long time ago, they can definitely follow Luo Yu's narration speed.

What Luo Yu talked about mainly focused on the first part of the topic, that is, issues related to quaternary quadratic types.

For this part, Luo Yu built a quite complete and detailed structure framework of the topic.

At least in theory, the other five people couldn't hear anything wrong with it.

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

I don’t know whether it’s intentional or because I didn’t have time to prepare. In short, the framework explained is not as perfect as the first part.

After Luo Yu, a student from Jiangzhe University spoke.

Like Luo Yu, the research framework for the first part of the project is quite complete, but the research framework for the second part of the project seems a bit shoddy, and it obviously seems to be rushed.

On the Yanda side, the classmate named Niu Zilin spoke third.

To put it simply, in the first part of the simple topic, the views and ideas explained by Luo Yu and Niu Zilin have many similarities, as do the topic frameworks they built.

The project framework described by the classmate from Jiangzhe University seemed a little more complicated than that of Luo Yu and Niu Zilin.

To measure it numerically, it's about one-third more work.

In the end, the six people decided to use Luo Yu's framework as the main one, and then combine the better parts of Niu Zilin's framework into it to form a brand new framework.

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

During this process, the three teachers Gu Lu rarely spoke at the side, and more they observed the performance of the six people in this process.

After completing the framework, Luo Yu turned to look at Gu Lu and the others, and said politely, "Three teachers, we have completed the discussion on the first part of the subject framework. I hope you can give us some suggestions for improvement."

This is one of the purposes for Gu and Lu to attend this meeting, so they will naturally not refuse.

In fact, in the view of the three of them, the research framework that the six people discussed after such a long time was full of loopholes.

Teacher Tao and the teacher from Jiangzhe University on the other side looked at Gu Lu with a smile, obviously wanting to give Gu Lu, the host, a chance to show off.

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

Gu Lu shrugged and said with a smile, "Let me just make a few comments."

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

"First point." Gu Lu raised his first finger, "You think the asymptotic formula for solving the quadratic form is too ideal. Because currently, using the existing method, you want to directly obtain the quadratic form.

The asymptotic formula of the type is quite difficult. This is not only a question of method, but also a question of the amount of operations."

"Therefore, my suggestion is to derive the quadratic form of the quaternary form through the asymptotic formula of the mixed form of the quadratic and cubic form of the ternary form: (m1^2m2^2m3^3,m1^2m2^2m3^3m4^3)

Asymptotic formula.”

Everyone was inspired by Gu Lu's words, and they all nodded in agreement like chickens pecking at rice. At the same time, they were surprised that Gu Lu could find their shortcomings so keenly.

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

"Theorem 1 and Theorem 2 are not as long as they meet the 'almost equal' conditions and the structure of the quaternary quadratic form as you imagined, and they should also be related to asymptotes."

"For example, s(x)=2k1l1x4log x(k1l2k2l1)x4o(x7/2ε), where k1=2ζ(2)

/7ζ(3),k2=4ζ(2)/7ζ(3)(γ12/72ζ(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 is that the use of the prime number theorem on the complex plane is well known..."

Gu Lu kept talking rapidly.

"The fourth point..."

"The fifth point..."

…

For more than ten minutes, Gu Lu pointed out more than a dozen shortcomings in everyone's framework.

Moreover, every problem actually exists, and there is no such thing as Gu Lu trying to find faults in the eggs.

This result made everyone even more ashamed.

They realized that this almost perfect project framework that made them so proud was actually full of loopholes in the eyes of this teacher.
Chapter completed!