"This, this, and this..."

Within the search scope, all documents that Chen Zhou thought might be useful.

They were all downloaded by him in batches.

For others, this may be the stupidest and clumsiest method.

But for Chen Zhou, sorting out a large number of documents is the best way for him to form a knowledge network.

Coupled with the correction of wrong question sets, the density of this knowledge network is simply unmatched.

And after sorting out the content just now, Chen Zhou suddenly felt a strange feeling.

It was a different feeling than when he had previously studied analytic number theory, which was a difficult problem.

But Chen Zhou couldn't quite explain what it felt like.

Shaking his head slightly, Chen Zhou stopped thinking about it.

Put the filled scratch paper aside and replace it with a new one.

After replacing the refill that had run out of ink, Chen Zhou began the next stage of combing.

As for the current time, the lunch that I originally planned to have on time, and the email that Professor Artin didn't know whether he sent or not, are not important anymore.

Now, Chen Zhou only sees the literature in front of him, only the L function, and only the Riemann zeta function.

There are only algebraic problems and algebraic geometry problems.

Even the brother he longed for was temporarily forgotten.

Opening a newly downloaded document, Chen Zhou quickly scanned it.

Now Chen Zhou, with his Level 7 mathematics, can read documents surprisingly quickly.

However, so far, only Yang Yiyi knows this efficient method of reading literature.

When they were at Yan University, Zhao Qiqi, Zhu Mingli, and Li Li had only seen the weakened version.

They haven't seen the enhanced version after Mathematics was upgraded to Level 7.

It is worth mentioning that it was the continuous improvement of mathematics level that enabled Chen Zhou to embark on the path of mathematics.

There is nothing new in this document, it is mainly about the Riemann zeta function.

After Chen Zhou read it, he would just "X" it away.

But as soon as the mouse moved to the "X" in the upper right corner, Chen Zhou's hand stopped.

The left mouse button has not been pressed.

"Properties of the Riemann zeta function..."

"The modular form of 1/2..."

Chen Zhou's thinking was diverged from the documents in front of him.

"What is the property of the second condition of the Riemann zeta function? If you look carefully at the proof of this property, you will find that? This proof essentially uses a very special automorphic form of symmetry? That is, the weight

1/2 mold form..."

Thinking of this? Chen Zhou looked at the documents in front of him again.

The content of the documents in front of me supports a fact.

This fact is the proof of the second condition of the Riemann zeta function for almost all known L functions over the entire domain.

All use the automorphic form!

Chen Zhou picked up the pen and circled the four words "autonomous form" on the previous piece of draft paper.

Immediately, on a new draft paper, I annotated the three keywords "automorphic form", "property 2 of the Riemann zeta function", and "modular form of weight 1/2".

After finishing this? Chen Zhou closed this document and opened the next document.

In fact, after sorting it out until now, the scope of the content Chen Zhou investigated has already exceeded the scope of the topic "Linear representation of the Artin L function of the Galois group".

In other words, the study of this subject? It is only a part of Chen Zhou's sorting out the content.

With the combing of the content? Chen Zhou's strange feeling is getting heavier.

"This literature? Is it a bit delicious?"

One after another, Chen Zhou finally found a different article.

Sliding the roller of the mouse and pull the literature to the top.

After glanced at the author and time of the literature, Chen Zhou whispered: "No wonder I said that the taste is different ..."

The time of publishing this literature is very age.

The author of this literature alone, two famous mathematicians of the Japanese country, Shimura Goro and Tana Tana.

As soon as the names of the two people heard it, they knew that time was long.

Chen Zhou was also a little surprised. Why did he searched for such a period of age?

I glanced at the search page of the browser. It turned out that when Chen Zhou searched, he only chose the search range and did not choose the time of the literature.

However, fortunately, because there was no time to choose the literature, Chen Zhou did not miss such an excellent literature.

The content of this literature is exactly when Chen Zhou sorted out the content, the Tanushan-Shimura conjecture written.

But the content is not just Guishan-Shimura conjecture.

Speaking of which, Tanamura Koshimura and Tanama's Guishan-Shimura conjecture that it is really beautiful to connect the ellipse curve to the pattern.

How about the head of mathematicians, only the moment when the inspiration broke out?

In addition to the content of this literature, there is also the content of the BSP; L function outside the contents of Gushan-Shimura.

From the special circumstances of the elliptical curve, Shimura Goro and Tanama raised a guess.

They guess the BSP; L function can be constructed from a certain type of self -definition.

In the literature, Shimura Goro's method is to a large extent from the algebraic geometry.

From the specific calculation, he saw some exquisite special structures.

But because of this, his method is too specific that it is difficult to directly promote it to the general situation.

In the literature that Chen Zhou, he turned around and quickly locked the target.

Quickly double -click the left mouse button and open the literature.

Chen Zhou glanced and said softly: "Although Shimura Woron has not been promoted to the general situation, Professor Langlaz has done it ..."

On the draft paper, Chen Zhou began to sort out the contents of these two documents.

Professor of Langlazz to the general situation is the famous Langlazest program in modern mathematics.

Langlaz's insight is that he can see the kernel of the composition behind these structures.

He systematically expressed the infinite dimension of the algebraic group to the theory of numbers, and found a global program that promoted to the general situation.

On the draft paper, Chen Zhou wrote:

[It is generally considered to be composed of two parts, and the first part is called mutually counter -guesses. It describes the corresponding relationship between the theory and the theory.

The most general guess is that Motive is equivalent to a considerable part of the form.

In particular, it pointed out that Gallowa said that it should be equivalent to the representative of the algebra.

Therefore, the BSP; L function is equivalent to the self -defense L function.

The second part is called it, the letter Zi Guess, it describes the connection between different groups ...]

After this passage was written, Chen Zhou looked at this passage like this, and he was so embarrassed.

I have to say that the meaning of the Langlanz program is far -reaching.

It can prove the property 2 of the Riemann zeta function for the most general L function.

And derived a series of difficult conjectures, such as Artin's conjecture.

After decades of hard work, mathematicians have made great progress in their understanding of the Langlands Programme.

Outstanding representative scholars include Fields Medal winner Vladimir Delinfeld, Laurent Laforgue and Professor Wu Baozhu.

However, it is still very far away from a complete program.

But it must be mentioned that the scope of the Langlands Program is still expanding.

By analogy with the classic program, mathematicians have developed geometric Langlands and p-adic Langlands.

Even in physics, Professor Edward Witten proposed a similar Langlands duality.

They involve very different fields and use very different methods.

But they all show very deep similarities.

From different perspectives, it enriches the Langlands program itself.

One of the latest and noteworthy developments in the Langlands Program comes from the ongoing work of the talented German mathematician Peter Schulz.
To be continued...