Chapter 254

The cross-school project has been started for half a month.

In the past half month, both Luo Yu's research group and Bao Zi's research group have made good progress.

Especially Bao Zi.

Several major breakthroughs have been made on the problem of the mean Fourier coefficient of the automorphic l function whose variables are ternary quadratic forms.

There is a document on the desk.

It records in detail a series of progress Bao Zi has made so far in the process of studying the problem of the mean Fourier coefficient of the automorphic l function.

Gu Lu glanced briefly, then nodded with satisfaction.

In general, the progress on Bao Zi's side was faster than Gu Lu expected.

Gu Lu originally thought that if Bao Zi's progress reached 10 in about half a month, it would be considered good.

But now it seems that this estimate is still somewhat conservative.

Regarding the research on the mean value of Fourier coefficients in the project, Bao Zi’s progress is almost 15.

If we continue at this efficiency, it will not take half a year, but only about four months, and Bao Zi will be able to complete the work.

Gu Lu still doesn't know the research progress of Luo Yu at Jinling University, so he can't make a comparison.

But the research progress on Bao Zi's side can definitely not be called slow.

Gu Lu just flipped through the documents on the table while waiting for Bao Zi to come back.

Ten minutes later.

"Teacher, I'm back!"

Before anyone arrives, the sound comes first.

After hearing the sound, Gu Lu looked up and saw Bao Zi jumping in, holding a packing bag in his hand.

The packing bag contained several large buns, which must have been Baozi's breakfast.

Bao Zi raised the bag in his hand and said, "Teacher, do you want to eat steamed buns? The ones stuffed with beef."

Gu Lu smiled and waved his hand, "No, I've already had breakfast."

Bao Zi pulled up a chair and sat next to Gu Lu. Ah Wu bit off half of a bun and said vaguely while eating, "Teacher, can you give me some guidance on the problem I encountered now?"

.”

"Are you sure it's now?" Gu Lu pointed at the unfinished bun in Bao Zi's hand.

Bao Zi nodded, "This saves time."

"Then tell me."

Under Gu Lu's instruction, Bao Zi talked about a problem she encountered during her research a few days ago.

Bao Zi studies the problem of the mean Fourier coefficient of the automorphic l function whose variables are ternary quadratic forms.

In accordance with the research plan formulated in the project framework.

To solve this problem, two functions with variables n need to be established to represent the Fourier coefficients of the maass cusp form and the holomorphic cusp form respectively.

Then, using the dirichlet rational approximation theorem and Chauchy's inequality, we get the estimate of t on the main interval and the estimate of s1 on the remainder interval.

Bao Zi is stuck at this step.

To put it simply, Bao Zi has not figured out how to use the Fourier coefficients of the maass cusp form and the pure cusp form to accurately obtain the estimate of t on the main interval and the estimate of s1 on the remainder interval.

"That's it..."

Gu Lu touched his chin and nodded in understanding.

Bao Zi is right, this place is indeed one of the difficulties of this subject.

Once it is not handled well, it is easy to lose all your previous efforts.

However, this is not a problem for Gu Lu.

After saying that, Bao Zi took a bite of the bun and squinted his eyes comfortably, looking very satisfied.

"Well, I've been thinking about it all night, but I don't have any clue. It's very sad."

Bao Zi said something vaguely, but there was no trace of worry on his face.

"Teacher, this problem is not difficult for you, right?" Bao Zi stared at Gu Lu with bright eyes.

Gu Lu nodded.

Bao Zi said with a smile, "Then I'll ask the teacher to clear up the confusion."

Gu Lu smiled helplessly and took a blank piece of draft paper from the table.

He took out a fan's carbon pen from the pen holder. After pondering for a few seconds, Gu Lu wrote six big characters on the paper.

"What's wrong with the ball?" Bao Zi exclaimed.

Gu Lu smiled faintly and said, "That's right, it's just an issue with the timing of the ball."

The full name of the integer point problem within the sphere is the prime number distribution problem of integer points within the sphere.

This is a well-known problem in the field of analytic number theory.

However, this problem has not yet been completely solved.

However, although the problem of integer points within the sphere has not been completely solved, it does not prevent mathematicians from using its related knowledge to solve other mathematical problems.

Take, for example, the problem at hand.

Currently, the problem that Bao Zi is encountering is not the only solution using the integer point problem within the sphere.

But after comparing several options, Gu Lu believed that this was the simplest option.

On Bao Zi's side, after Gu Lu reminded him, he suddenly realized.

There is a lot of knowledge related to the whole point problem within the ball.

But there is only one piece of knowledge related to the research content of this topic.

That was a formula proposed by two Chinese mathematicians in the 1990s, using the ternary quadratic form and based on the integer point problem within the sphere:

πΛ:∑Λ8c3i3xyilyigx)

Of course, the prerequisite for this formula to be established is a0.

The formula is not complicated, but it is one of several major research results on the problem of integer points within the sphere.

Because it reveals the problem of the distribution of prime numbers at part of the whole point in the sphere.

Although he vaguely guessed something, Bao Zi was not sure, so he looked at Gu Lu inquiringly.

Gu Lu stopped trying to sell things off.

Write down a line of formula on the paper with a few swipes.

πΛ:∑Λ8c3i3xyilyigx)

This formula is exactly what Bao Zi guessed.

However, Bao Zi did not speak rashly, but waited for Gu Lu's next words.

Gu Lu circled 'c3' and 'i3' in the formula and explained, "These two symbols, c3 represents the singular series in the problem of integer points in the sphere, and i3 represents the singular integral. We can start with this...

"

"...Based on the above premise, the formula πΛ: (omitted) can be obtained from the formula π312c3i3∫t0.5/lyigtdtyix)."

Gu Lu spoke very quickly, but Bao Zi next to him could easily keep up with Gu Lu's speed without any pressure.

You can even take a few bites of steamed buns.

Bao Zi understood most of Gu Lu's train of thought.

To put it simply, it uses the formula of the ternary quadratic integer point problem in the sphere to obtain the singular series and singular integral.

Then on the basis of singular series and singular integrals, the formula for the mean problem related to the divisor function was obtained.

Sure enough, the last step that Gu Lu talked about was the derivation of the mean problem of the divisor problem.

"... Finally, based on the previous five formulas, we can derive a formula for the mean problem related to the divisor function, that is..."

Since there was no preparation in advance, Gu Lu calculated this formula on the spot.

After briefly going over it in his mind, Gu Lu wrote down the final formula on paper.

s:∑d8ζ/5ζx3lyigxyi.

"Hiss, this formula..."
Chapter completed!