Volume 1: Student Life Chapter 443: Tiny Mathematics
"This, this, and this..."
All literature within the search scope that Chen Zhou thinks may be useful.
He downloaded all of them in batches.
For others, this may be the stupidest and clumsiest method.
But for Chen Zhou, sorting out a large amount of literature is the best way for him to form a knowledge network.
Coupled with the correction of wrong questions in the collection, the density of this knowledge network is simply unmatched.
And after sorting out the content just now, Chen Zhou suddenly had a strange feeling.
It was a different feeling from when he was studying analytic number theory and it was a difficult problem.
But Chen Zhou couldn't explain what this feeling was.
Shaking his head slightly, Chen Zhou didn't think about it any more.
Put the filled draft paper aside and replace it with a new one.
After replacing the pen refill which had run out of ink, Chen Zhou began the next stage of sorting.
As for the current time, the lunch that I had originally planned to have on time, and the email that Professor Atin had not yet sent, none of them mattered anymore.
Now, in Chen Zhou's eyes, there are only 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 his beloved Ge Chai was temporarily forgotten.
Chen Zhou opened a newly downloaded document and scanned it quickly.
Now, Chen Zhou, with his level 7 mathematics, can read literature at an astonishing speed.
However, so far, only Yang Yiyi knows this efficient way of reading literature.
Previously at Yan University, Zhao Qiqi, Zhu Mingli and Li Li had only seen a weakened version.
They haven't seen the enhanced version of Mathematics after it reaches Level 7.
It is worth mentioning that it was the continuous improvement of his mathematics level that enabled Chen Zhou to embark on the journey of mathematics.
There is nothing new in this paper, it is mainly about the Riemann zeta function.
After reading it, Chen Zhou would just cross it out.
But as soon as the mouse moved to the "X" in the upper right corner, Chen Zhou's hand stopped.
The left mouse button is not pressed.
"The properties of the Riemann zeta function..."
"The modular form of the weight 1/2..."
Chen Zhou's thoughts diverged from the documents in front of him.
"If you look carefully at the proof of the second property of the Riemann zeta function, you will find that it actually uses a very special symmetry of the automorphic form, that is, the modular form of weight 1/2..."
Thinking of this, Chen Zhou looked at the document in front of him again.
The content of the document before us proves a fact.
This fact is that, in fact, almost all known L-functions over global fields prove the second condition of the Riemann zeta function.
All use automorphic forms!
Chen Zhou picked up the pen and circled the four words "autoconservative form" on the previous draft paper.
Then, I annotated the three key words "automorphic form", "properties of Riemann zeta function 2", and "modular form of weight 1/2" on a new draft paper.
After doing all this, Chen Zhou closed this document and opened the next one.
In fact, after sorting out the content up to now, Chen Zhou's research scope has long exceeded the scope of the topic of "Linear representation of Artin's L-function of the Galois group".
In other words, the research on this topic is only a part of the content that Chen Zhou sorted out.
As he sorted out the content, Chen Zhou's strange feeling became stronger and stronger.
"This document? It has some flavor, doesn't it?"
After reading one document after another, Chen Zhou finally found one that was different.
Slide the mouse wheel to move the document to the top.
Glancing at the author and time of the document, Chen Zhou whispered, "No wonder I said the taste is different..."
The publication time of this document is quite old.
The authors of this document are two famous Japanese mathematicians, Goro Shimura and Yutaka Taniyama.
Just hearing the names of these two people, you can tell how long ago they were together.
Chen Zhou was also a little surprised. How could he have found such old documents?
After taking a glance at the browser's search page, it turned out that Chen Zhou had only selected the search range when searching, but did not select the time of the document.
However, fortunately, because there was no time to select the literature, Chen Zhou did not miss such an excellent literature.
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 not just the Taniyama-Shimura conjecture.
By the way, the Taniyama-Shimura conjecture proposed by Goro Shimura and Yutaka Taniyama is really amazing because it can link elliptic curves and modular forms.
Otherwise, why do they say that a mathematician's brain is only at the moment of inspiration?
In addition to the Taniyama-Shimura conjecture, this paper also contains the content of motivational L-function.
From the special case of elliptic curves, Goro Shimura and Yutaka Taniyama proposed a conjecture.
They speculated that motivic L functions can be constructed from some kind of automorphic form.
In the literature, Goro Shimura's method is largely derived from algebraic geometry.
He saw some exquisite special structures from the specific calculations.
But because of this, his method is too specific to be directly generalized to general situations.
Chen Zhou searched through the downloaded documents and quickly locked on the target.
Quickly double-click the left mouse button to open the document.
Chen Zhou took a look and said softly: "Although Goro Shimura did not generalize it to general situations, Professor Langlands did it..."
On the draft paper, Chen Zhou began to sort out the contents of the two documents.
What Professor Langlands extended to the general case is the famous Langlands program in modern mathematics.
Langlands' insight was that he saw the representation-theoretic kernel behind these structures.
He systematically introduced the infinite-dimensional representation of algebraic groups into number theory and found a global program that could be extended to general cases.
On the draft paper, Chen Zhou wrote:
[It is generally believed that the Langlands program consists of two parts. The first part is called the reciprocity conjecture, which describes the correspondence between number theory and representation theory.
The most general guess is that Motive is equivalent to a considerable number of automorphic forms.
In particular, it points out that Galois representations should be equivalent to representations of algebraic groups.
Therefore, the motivic L function is equivalent to the automorphic L function.
The second part is called the functor conjecture, which describes the connection between representations of different groups...]
After finishing writing this paragraph, Chen Zhou just looked at it in a daze.
It has to be said that the Langlands Program is of far-reaching significance.
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 the Artin conjecture.
After decades of hard work, mathematicians have made great progress in their understanding of the Langlands Program.
Outstanding representative scholars include Fields Medal winners Vladimir Drinfeld, Laurent Laforgue and Professor Wu Baozhu.
However, it is still a long way from a complete program.
But it must be mentioned that the scope of the Langlands Program is still expanding.
By analogy with the classical program, mathematicians have developed geometric Langlands and paradic Langlands.
Even in physics, Professor Edward Witten proposed a similar Langlands duality.
They involve very different areas and use very different methods.
But they all show very deep similarities.
From different perspectives, the Langlands Program itself is enriched.
One of the latest and most noteworthy advances in the Langlands Program comes from the ongoing work of the talented German mathematician Peter Schulze.
Schultz used the case of the analogy function field based on the paradic geometry he developed to prove the case of the local number field.
Thinking of this, a smile appeared on Chen Zhou's lips.
Then, he took out a new piece of draft paper and wrote quickly on it.
Chen Zhou finally understood what that strange feeling was.
At the beginning, he only intended to sort out the research content involved in the topic of "Linear representation of Artin's L-function of the Galois group".
But as time went by, Chen Zhou actually sorted out modern mathematics in a rough but complete way, using Riemann zeta function and L function as clues.
It also lists the important problems in modern mathematics, especially in the field of algebraic geometry.
This includes algebraic geometry, algebraic topology, algebraic number theory, harmonic analysis, automorphic forms, flat cohomology, Galois representation, Motivic L-function, Langlands program, BSD conjecture, Beilinson conjecture, Artin conjecture, and so on.
What Chen Zhou didn't expect was that all the information he sorted out actually had a connection.
This also made Chen Zhou understand something from another perspective.
That is, in today's mathematics, there is no independent branch of mathematics in the pure sense.
Each branch of mathematics is cross-cutting and interconnected.
Chen Zhou also felt a little relieved.
I am glad that I have constructed the mathematical tool of distribution deconstruction and am constantly improving it.
Soon, Chen Zhou put down the pen in his hand.
A schematic diagram appeared on the draft paper.
Chen Zhou presented all this content in a complete manner using diagrams.
There are conjectures and known results.
However, from now on, almost all the speculations in the content sorted out by Chen Zhou are still very far away.
Each one may be enough to exhaust a person's life energy.
However, it is precisely its difficulty and depth that attracts countless people.
To some extent, mathematicians and explorers are actually the same kind of people.
To be honest, from a certain perspective, both the Cramer conjecture and the Gerbov conjecture that Chen Zhou had previously solved are just a small part of analytic number theory.
In the context of modern mathematics, it is really nothing.
It can be said to be the mathematics of the small.
But it is precisely the smallness of each step and each person that makes great mathematics possible.
Looking at the picture in front of him, the strange feeling in Chen Zhou's heart had disappeared.
When you face your thoughts and feelings, everything becomes clear.
A smile appeared on Chen Zhou's lips, and he suddenly had a strange idea.
Should he go and thank this senior sister Nott?
because……
If it weren't for Senior Nott's invitation, he wouldn't have come back to sort out this part of the content.
If he hadn't sorted out this part of the content, he wouldn't have been able to come up with the picture in front of him.
The unresolved content in this picture is probably the series of problems mentioned by Noether, including the Langlands Program.
Originally, Nott wanted to win over Chen Zhou and conduct research together.
Made efforts for the mathematical revival of the Noether family.
But now, it indirectly pointed out the future direction for Chen Zhou.
Of course, this is also based on the premise that Chen Zhou can solve Ge Guess first.
If Chen Zhou can successfully solve the Brother's conjecture, then that will be the future direction of mathematical research.
It is most likely what he sorted out today.
Outside the window, it had darkened.
At this moment, Chen Zhou realized that he had not gone to have lunch because he was immersed in the world of mathematics.
This is the third time this has happened since Yang Yiyi left.
And Yang Yiyi had only been away for a week.
"Oh, no wonder they all want to get married..."
Chen Zhou misses the days when he and Yang Yiyi supervised each other, learned from each other, worked on projects together, and were taken care of by each other.
I looked at my watch and it was already past 9 o'clock in the evening.
In other words, Chen Zhou has been working for nearly 12 hours since he came back!
After tidying up his things, Chen Zhou stood up and stretched his muscles a little.
When you are concentrating, you don't feel much.
With this relaxation, the fatigue from sitting for a long time to study suddenly came up.
"Fortunately, I run regularly to exercise..." Chen Zhou said in a low voice.
However, what responded to him was the cry of his stomach.
Chen Zhou's expression froze for a moment, and he said helplessly, "What a pity, exercise doesn't help you stay hungry..."
Fortunately, it was not too late at this point, so Chen Zhou, who went out to find food, had a pretty good midnight snack.
When he returned to the dormitory, Chen Zhou did not rush to sit back at his desk.
Instead, I took a hot bath to relieve the fatigue of the day.
Only then did I devote myself again to the task of finding the rubber ball.
Although Chen Zhou did not encounter Ge Guess today, he has been dealing with the world of mathematics for the whole day.
I don't want to spend my evening time on math anymore.
Therefore, Chen Zhou started to study the topic of rubber ball experiment again.
Now, he has almost completed the theoretical content of the strange quantum number glue ball.
The content of this part is far less than the research content of conventional quantum number glueball.
The reason is that in previous research, physicists rarely involved the study of strange quantum number glueballs.
As for why it is rarely involved...
One reason is that the exotic quantum number glueballs are relatively heavy.
Another reason is that computational analysis is relatively complex.
For example, for 0, the glueball is still blank under the QCD summation rule framework.
But this is the reason why Chen Zhou doesn't need to worry the least.
The experimental projects he participated in and their final perfect results.
Almost all of it was achieved through his calculations, combined with continuous trial and error to find the right direction.
Therefore, the theoretical research on the strange quantum number glueball aroused Chen Zhou's great interest.
Any goal that can be achieved by calculation.
Chen Zhou felt that those were just small goals.
