"This, this, and this ......"

Within the scope of the search, all the literature that Chen Zhou thinks may be useful.

He downloaded them all in batches.

This is perhaps the stupidest and most clumsy method for others.

But for Chen Zhou, combing through a large number of literature is the best way for him to form a knowledge network.

Coupled with the correction of the wrong problem set, the density of this knowledge network is simply invincible.

And after combing through the content just now, Chen Zhou suddenly had a strange feeling.

It's a different feeling from when he was working on the problem of analytic number theory.

But Chen Zhou couldn't say what it felt like this.

Shaking his head slightly, Chen Zhou didn't think much about it.

Set this filled piece of scratch paper aside and replace it with a new one.

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

As for the current time, it doesn't matter if I was going to have lunch on time, and if Professor Atin doesn't know if he sent the email.

Now, in Chen Zhou's eyes, there is only the literature in front of him, only the L function, and only the Riemann ζ function.

There are also only problems with algebra and problems with algebraic geometry.

Even the brother who was in his heart was temporarily left behind.

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

Now Chen Zhou, with Lv7 mathematics, the speed of reading literature is also surprisingly fast.

However, this efficient way of reading literature has so far only been known to Yang Yiyi.

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

The enhanced version of mathematics after upgrading to Lv7, they haven't seen it yet.

It is worth mentioning that it is the continuous improvement of mathematics level that makes Chen Zhou open the journey of mathematics.

There is nothing new in this literature, mainly about the Riemann ζ function.

After Chen Zhou finished reading it, he had to "X" it out casually.

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

Left mouse button, not pressed.

"Properties of the Riemann ζ Function......"

"Modular ...... of 1/2 of the right"

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

"The property of the second condition of the Riemann ζ function, if we look closely at the proof of this property, we will find that this proof essentially uses a very special kind of symmetry in the form of self-defense, that is, the modular form of weight 1/2......"

Thinking of this, Chen Zhou looked at the literature in front of him again.

The content of the literature in front of us corroborates a fact.

The fact that the L-function on virtually almost all known global domains is a proof of the second condition of the Riemann ζ function.

All use the form of self-defense!

Chen Zhou picked up the pen and circled the words "self-disciplined form" on the previous scratch paper.

Immediately, on the new scratch paper, the three key words "self-defending form", "properties of Riemann ζ function 2", and "modular form of weight 1/2" were annotated.

After doing this, Chen Zhou closed this document and opened the next one.

In fact, up to now, the scope of the content investigated by Chen Zhou has long gone beyond the scope of the topic of "linear representation of the Atin L function of the Galois group".

In other words, the research on this topic is only a part of Chen Zhou's combing content.

As the content was sorted out, Chen Zhou's strange feeling became heavier and heavier.

"Does this document smell a little bit?"

After one document after another, Chen Zhou finally found a different one.

Slide the scroll wheel of the mouse to pull the document to the top.

Glancing at the author and time of the document, Chen Zhou said in a low voice: "No wonder I said that the taste is different......

The publication time of this document is very old.

The authors of this document alone, two famous mathematicians of Japan, Goro Shimura and Yutaka Taniyama.

As soon as you hear the names of these two people, you know that time is long.

Chen Zhou was also a little surprised, how could such a document with a sense of age be searched by him?

Glancing at the search page of the browser, it turned out that when Chen Zhou searched, he only selected the search scope, and did not select the time of the literature.

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

The content of this document is exactly the Taniyama-Shimura conjecture that Chen Zhou wrote when he was sorting out the content just now.

But the content is more than just the Taniyama-Shimura conjecture.

Speaking of which, the Taniyama-Shimura conjecture proposed by Goro Shimura and Yutaka Taniyama can connect elliptical curves with modular forms, which is really beautiful.

How else can we say that the head of a mathematician is only in the moment when inspiration bursts?

In addition to the Taniyama-Shimura conjecture, the content of this document also contains the content of the motivic L function.

From the special case of elliptical curves, Goro Shimura and Yutaka Taniyama came up with a guess.

They guessed that the motivic L function could be constructed from some kind of self-defeating form.

In the literature, Goro Shimura's method is largely derived from algebraic geometry.

From the specific calculations, he saw some delicate special structures.

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

Chen Zhou rummaged through the downloaded literature and quickly locked on the target.

Quickly double-click the left mouse button to open the document.

Chen Zhou glanced at it and said softly: "Although Shimura Goro has not been generalized to the general situation, Professor Langlands has done ......"

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

What was popularized by Professor Langlands to the general situation is the well-known Langlands program in modern mathematics.

Langlands' insight lies in the fact that he sees the representational kernel behind these structures.

He systematically introduced the infinite-dimensional representation of algebraic groups into number theory, and found an overall program that can be generalized to the general situation.

On the scratch paper, Chen Zhou wrote:

[It is generally believed that the Langlands program consists of two parts, the first part is called the inverse conjecture, which describes the correspondence between number theory and representation theory.]

The most general guess is that Motive is equivalent to a fair share of the self-contained form.

In particular, it states that the Galois representation should be equivalent to the representation of algebraic groups.

Therefore, the motivic L-function is equivalent to the self-defending L-function.

The second part is called the functal conjecture, which describes the connections between representations between different groups......]

After this passage was written, Chen Zhou looked at this passage like this, stunned.

It has to be said that the significance of the Langlands program is far-reaching.

It can be used for the most general L-function, proving the properties of the Riemann ζ function2.

And derive a series of difficult conjectures, for example, the Artin conjecture.

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

Distinguished scholars include Fields Medal winners Vladimir Delpenferd, Laurent Laforgue and Professor Wu Baozhu.

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

However, it must be mentioned that the scope of the Langlands program is still expanding.

By analogy with the classical program, mathematicians developed the geometric Langlands and the p-ADIC Langlands.

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

They involve very different areas and use very different approaches.

But they all show a very deep similarity.

From different perspectives, it enriches the Langlands program itself.

One of the most recent, and noteworthy developments, in the Langlands Program comes from the ongoing work of the brilliant German mathematician Peter Schulz.

Schultz uses the case of the p-adic geometric analogy function field developed by him to prove the case of the local number field.

Thinking of this, a smile appeared on the corner of Chen Zhou's mouth.

Immediately, he took out a new piece of scratch paper again and quickly wrote on it.

Chen Zhou finally knew what that strange feeling was before.

At the beginning, he just planned to sort out the research content involved in the topic of "linear representation of the Atin L-function of the Galois group".

But with the passage of time, Chen Zhou is actually like this, although it is rough, but it is quite complete, using the Riemann ζ function and the L function as clues, combing through modern mathematics.

And the important problems in modern mathematics, especially in the field of algebraic geometry, are listed.

These include algebraic geometry, algebraic topology, algebraic number theory, harmonic analysis, automorphism, flat cohomology, Galois representations, Motivic L functions, Langlands program, BSD conjecture, Bellinson's conjecture, Artin conjecture, and so on.

What Chen Zhou didn't expect was that all the content he sorted out had a trace of connection.

This also made Chen Zhou understand one thing from another angle.

That is, there is no independent branch of mathematics in the pure sense of the word.

Each branch of mathematics is intersecting.

Chen Zhou also had a hint of happiness.

I am glad that I have constructed a mathematical tool called distribution deconstruction, and I am constantly refining it.

Soon, Chen Zhou stopped the pen in his hand.

On scratch paper, a schematic diagram appeared.

Chen Zhou showed these contents in a complete illustrated way.

There are conjectures in it, and there are also known results.

However, from the current point of view, almost all the conjectures in the content that Chen Zhou sorted out are still very far away.

Each one may be enough to drain a person's life's energy.

However, it is precisely its difficulty and profundity that attracts countless people.

In a way, mathematicians and explorers are the same kind of people.

From a certain point of view, whether it is the Kramel conjecture or the Jebov conjecture that Chen Zhou solved before, they are only a small part of analytic number theory.

In modern mathematics as a whole, it's really nothing.

The mathematics of insignificance, so to speak.

But it is precisely this insignificance of each step, the insignificance of each person, that makes great mathematics.

Looking at the picture in front of him, the strange feeling in Chen Zhou's heart has disappeared.

When you face up to your thoughts and feelings, everything suddenly becomes clear.

A smile appeared at the corner of Chen Zhou's mouth, and he suddenly had a strange thought.

Shouldn't he be thanking this Knott-senpai?

Because......

If it weren't for Sister Notte's invitation, he wouldn't have come back to sort out this part.

If he hadn't sorted out the content of this part, he wouldn't have been able to figure out the picture in front of him.

And the unresolved content on this picture is probably a series of problems in Noether's mouth, including the Langlands Program.

Originally, Knott hoped to win over Chen Zhou and conduct research together.

For the revival of mathematics of the Noether family, to make efforts.

But now, it indirectly pointed out the direction for Chen Zhou in the future.

Of course, this is also based on Chen Zhou's ability to solve the problem first.

If Chen Zhou can successfully solve the problem of Gechai, then the direction of mathematical research in the future.

There is a high probability that this is the content he sorted out today.

Outside the window, it was already dark.

At this time, Chen Zhou realized that he didn't go to lunch because he was immersed in the world of mathematics.

This is the third time since Yang Yiyi left.

And Yang Yiyi has only been away for a week.

"Alas, no wonder they all have to marry wives......"

Chen Zhou misses the days when he and Yang Yiyi supervised each other, learned from each other, worked on projects together, and lived by each other at the same time.

I looked at my watch, and it was already past 9 o'clock in the evening.

In other words, Chen Zhou has worked for nearly 12 hours since he came back!

After tidying up his things and standing up, Chen Zhou moved his muscles and bones a little.

When you're engrossed, you don't feel much.

This relaxation, the fatigue of sitting for a long time and studying, suddenly came up.

"Fortunately, I often run ......and exercise," Chen Zhou whispered.

However, in response to him was the cry of the Five Organs Temple.

Chen Zhou's expression was stunned for a moment, and he said helplessly: "It's a pity, I can't carry hunger when I exercise......"

Fortunately, at this point, it was not too late, and Chen Zhou, who went out to forage for food, had a good supper.

Back in the dormitory again, Chen Zhou was in no hurry to sit back at his desk.

Instead, I took a hot shower to soothe the tiredness of the day.

I once again devoted myself to the task of finding rubber balls.

Although Chen Zhou has not touched Gechai today, Chen Zhou, who has been dealing with the world of mathematics all day.

I don't want to spend my evenings in math anymore.

Therefore, Chen Zhou began to study the topic of rubber ball experiments again.

Now he is about to complete the theoretical content of the peculiar quantum number rubber ball.

The content of this part is far less than the research content of conventional quantum number rubber balls.

The reason is that physicists have rarely been involved in the study of exotic quantum number rubber balls in previous studies.

As for why it is rarely involved......

One reason is that the peculiar quantum number rubber ball is relatively heavy.

Another reason is that the computational analysis is relatively complex.

For example, the 0--glue ball is still blank under the framework of QCD summation rules.

But this is the reason why Chen Zhou doesn't need to worry the most.

The experimental subjects he has participated in, the final perfect results.

Almost all of them rely on his calculations, combined with the correct direction of trial and error, and finally achieve it.

Therefore, the theoretical research on the peculiar quantum number rubber ball has aroused Chen Zhou's great interest.

But everything that can be calculated to achieve the goal.

Chen Zhou felt that it was all small goals.