NOVEL NEXT Xueba starts with change
Chapter 443 Small Mathematics (4000-word chapter)
Chapter 443 Small Mathematics (4000-word chapter)
"This, this, and this..."
Within the scope of the search, all documents that Chen Zhou thinks may be useful.
All of them were downloaded by him in batches.
For others, this may be the stupidest and most clumsy 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 error correction of the wrong question set, the density of this knowledge network is simply invincible.
And after sorting out the content just now, Chen Zhou suddenly felt a strange feeling.
It was a different feeling from when he was studying analytic number theory as a difficult problem.
But Chen Zhou couldn't tell what it felt like.
Shaking his head slightly, Chen Zhou stopped thinking about it.
Put this filled scratch paper aside and replace it with a new one.
After replacing the refills that had run out of ink, Chen Zhou started the next stage of combing.
As for the current time, the lunch that I planned to have on time, and the email that Professor Arting didn't know whether to send or not, are not important anymore.
Now, in Chen Zhou's eyes, there are only the documents in front of him, only the L function, and only the Riemann ζ function.
There are also only algebraic problems and problems of algebraic geometry.
Even Brother Chai, whom he had been thinking about, was temporarily left behind.
Opening a newly downloaded document, Chen Zhou quickly scanned it.
The current Chen Zhou, relying on Lv7 mathematics, can read documents at an astonishingly fast speed.
However, so far, only Yang Yiyi knows about this efficient way of reading documents.
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 of Mathematics Level 7.
It is worth mentioning that it is also the continuous improvement of the mathematics level that made Chen Zhou start the journey of mathematics.
There is nothing new in this literature, mainly about the Riemann zeta function.
After Chen Zhou finished reading it, he would "X" 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 was not pressed down.
"The properties of the Riemann zeta function..."
"The modular form of 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 condition of the Riemann zeta function, you will find that this proof essentially uses a very special symmetry of the automorphic form, that is, the weight 1/2 modulus form..."
Thinking of this, Chen Zhou looked at the documents in front of him again.
The content of the document 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 on the overall field.
Both use the self-defense form!
Chen Zhou picked up a pen, and circled the four words "self-defense form" on the previous draft paper.
Immediately, on the new draft paper, the three key words "automorphic form", "property 2 of the Riemann zeta function", and "modular form of weight 1/2" were annotated.
After doing this, Chen Zhou closed this document and opened the next one.
In fact, after sorting it out so far, the scope of the content investigated by Chen Zhou has already exceeded the scope of the subject of "Linear representation of the Artin L function of the Galois group".
In other words, the research on this topic is just a part of the content that Chen Zhou sorted out.
As the content was sorted out, Chen Zhou's strange feeling became more and more serious.
"This document? Does it have a taste?"
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 the taste is different..."
The publication time of this document is very old.
The light is the author of this document, two famous mathematicians in Japan, Goro Shimura and Toyo Taniyama.
As soon as you hear the names of these two people, you can tell that it has been a long time.
Chen Zhou was also a little surprised. Why did he find all the documents with a sense of age?
Glancing at the search page of the browser, it turned out that when Chen Zhou was searching, he only selected the search range and did not have the time to select the literature.
However, fortunately, Chen Zhou didn't miss such an excellent document because he didn't have time to select the document.
The content of this document is exactly the Taniyama-Shimura conjecture written by Chen Zhou when he sorted out the content just now.
But the content is not just the Taniyama-Shimura conjecture.
Speaking of it, the Taniyama-Shimura conjecture proposed by Shimura Goro and Taniyama Toyo can connect elliptic curves and modular forms, which is really pretty.
How about a mathematician's brain only lies in the moment when inspiration bursts out?
The content of this document, in addition to the content of the Taniyama-Shimura conjecture, also contains the content of the motivation L function.
Goro Shimura and Yutaka Taniyama made a guess from the special case of elliptic curves.
They conjectured that the motivic L functions can all be constructed from some kind of automorphic form.
In the literature, Shimura Goro's method is largely derived from algebraic geometry.
From specific calculations, he saw some exquisite special structures.
But also because of this, his method is too specific to be directly generalizable to the general case.
Chen Zhou rummaged through the downloaded documents, 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 Goro Shimura didn't generalize it to the general situation, Professor Langlands did it..."
On the draft paper, Chen Zhou began to sort out the contents of these two documents.
What Professor Langlands extended to the general situation is the famous Langlands program in modern mathematics.
Langlands' insight was that he saw a representation-theoretic core behind these structures.
He systematically introduced the infinite-dimensional representation of algebraic groups into number theory, and found a global program that can be extended to general situations.
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 reciprocal conjecture, which describes the correspondence between number theory and representation theory.
The most general guess is that Motive is equivalent to quite a few automorphic forms.
In particular it states that Galois representations should be equivalent to representations of algebraic groups.
Thus the motivic L function is equivalent to the automorphic L function.
The second part is called the functor conjecture, which describes the connection of representations between different groups...]
After writing this passage, Chen Zhou just stared at this passage, dazed.
It has to be said that the Langlands program has far-reaching significance.
It can prove the property 2 of the Riemann zeta function for the most general L function.
And derive a series of difficult conjectures, for example, Artin's conjecture.
After decades of hard work, mathematicians have made great progress in their understanding of the Langlands program.
Outstanding representative scholars, including Fields Medal winner Vladimir Drinfeld, Laurent Laforgue and Professor Wu Baozhu.
However, it is still very far from a complete program.
But it must be mentioned that the scope of the Langlands program is still expanding.
Analogous to the classic program, mathematicians have developed geometric Langlands and p-adic Langlands.
Even in physics, Professor Edward Witten proposed a similar Langlands dual.
They touch on very different fields and use very different methods.
But they both exhibit a deep level of similarity.
From different perspectives, the Langlands Program itself is enriched.
A recent, and notable, development of the Langlands program comes from the ongoing work of the genius German mathematician Peter Schulz.
Schulz used the p-adic geometric analogy function field developed by him to prove the local number field.
Thinking of this, a smile appeared on the corner of Chen Zhou's mouth.
Immediately, he took out a new draft paper and quickly wrote on it.
Chen Zhou finally knew what the strange feeling was before.
At the beginning, he just planned to sort out the research content involved in the subject of "Linear representation of the Artin L function of the Galois group".
But with the passage of time, Chen Zhou turned out to be like this. Although it was rough, it was still relatively complete. Using the Riemann ζ function and L function as clues, he sorted out modern mathematics.
And list the important issues 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, Bellingson conjecture, Artin conjecture ,Etc., etc.
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, current mathematics does not have an independent branch of mathematics in a pure sense.
Every branch of mathematics is cross-integrated.
Chen Zhou was also a little lucky.
Fortunately, I have constructed the mathematical tool of distribution deconstruction, and I am constantly improving it.
Soon, Chen Zhou stopped the pen in his hand.
On the draft paper, a schematic diagram appeared.
Chen Zhou displayed these contents in a complete way with diagrams.
There are conjectures and 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 may be enough to drain a man's life's energies.
However, it is its difficulty and profoundness that have attracted countless people.
To some extent, mathematicians and explorers are actually the same kind of people.
To be honest, from a certain point of view, whether it is Kramer's conjecture or Jebov's conjecture that Chen Zhou solved before, it is only a small part of analytic number theory.
From the perspective of modern mathematics as a whole, it is really nothing.
It can be said that it is the mathematics of smallness.
But it is also the insignificance of each step and 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 your thoughts and feelings, everything suddenly becomes clear.
A smile appeared on the corner of Chen Zhou's mouth, and he suddenly had a strange idea.
Should he thank this senior Nott?
because……
If it wasn't for Senior Sister Nott's invitation, he wouldn't have come back to sort out this part of the content.
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 that Noether said, including the Langlands program.
Originally, Nott hoped to win over Chen Zhou and conduct research together.
Efforts have been made to revive mathematics for the Knott family.
But now, it indirectly pointed out the future direction for Chen Zhou.
Of course, this is also based on Chen Zhou being able to solve Brother Guess first.
If Chen Zhou can successfully solve my brother's guess, then the direction of mathematics research will follow.
There is a high probability that it is the content he sorted out today.
Outside the window, the sky has darkened.
At this time, Chen Zhou realized that he hadn't gone to lunch because he was immersed in the world of mathematics.
This is the third time since Yang Yiyi left.
And Yang Yiyi only left for a week.
"Oh, no wonder everyone wants to marry a wife..."
Chen Zhou really missed the days when he and Yang Yiyi supervised each other, learned from each other, worked on projects together, and lived under the care of each other.
I glanced at my watch, 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 stretched his muscles a little.
When you're fully focused, you don't feel much.
With this relaxation, the exhaustion from sitting for a long time and studying suddenly surged up.
"Fortunately, I often run and exercise..." Chen Zhou said in a low voice.
However, what responded to him was the ensuing cry from the Temple of the Five Viscera.
Chen Zhou's expression froze for a moment, and he said helplessly, "Unfortunately, you won't be hungry after exercising..."
Fortunately, it's not too late at this point. Chen Zhou, who went out to look for food, had a decent supper.
Back in the dormitory again, Chen Zhou was not in a hurry to sit back at the desk.
Instead, I went to take a hot bath first to relieve the fatigue of the day.
It was only then that I once again devoted myself to the subject of looking for glue balls.
Although Chen Zhou hasn't met Ge Guess today, he has been dealing with the world of mathematics all day long.
I don't want to spend the evening time on mathematics.
Therefore, Chen Zhou started the research on the glue ball experiment again.
Now he is about to complete all 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 glue balls.
The reason is that in previous studies, physicists rarely dealt with the study of strange quantum number glue balls.
As for why so little is involved...
One reason is that strange quantum number gumballs are relatively heavy.
Another reason is that the computational analysis is relatively complex.
For example, for 0—the glue ball is still blank under the framework of the QCD summation rule.
But this, on the contrary, was the last reason why Chen Zhou didn't need to worry.
The experimental subjects he has participated in have the final perfect results.
Almost all rely on his calculations, combined with the correct direction of constant trial and error, and finally realized it.
Therefore, the theoretical research on the strange quantum number glue ball has aroused Chen Zhou's great interest.
Any goal that can be achieved by calculation.
Chen Zhou felt that those were all small goals.
(End of this chapter)
"This, this, and this..."
Within the scope of the search, all documents that Chen Zhou thinks may be useful.
All of them were downloaded by him in batches.
For others, this may be the stupidest and most clumsy 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 error correction of the wrong question set, the density of this knowledge network is simply invincible.
And after sorting out the content just now, Chen Zhou suddenly felt a strange feeling.
It was a different feeling from when he was studying analytic number theory as a difficult problem.
But Chen Zhou couldn't tell what it felt like.
Shaking his head slightly, Chen Zhou stopped thinking about it.
Put this filled scratch paper aside and replace it with a new one.
After replacing the refills that had run out of ink, Chen Zhou started the next stage of combing.
As for the current time, the lunch that I planned to have on time, and the email that Professor Arting didn't know whether to send or not, are not important anymore.
Now, in Chen Zhou's eyes, there are only the documents in front of him, only the L function, and only the Riemann ζ function.
There are also only algebraic problems and problems of algebraic geometry.
Even Brother Chai, whom he had been thinking about, was temporarily left behind.
Opening a newly downloaded document, Chen Zhou quickly scanned it.
The current Chen Zhou, relying on Lv7 mathematics, can read documents at an astonishingly fast speed.
However, so far, only Yang Yiyi knows about this efficient way of reading documents.
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 of Mathematics Level 7.
It is worth mentioning that it is also the continuous improvement of the mathematics level that made Chen Zhou start the journey of mathematics.
There is nothing new in this literature, mainly about the Riemann zeta function.
After Chen Zhou finished reading it, he would "X" 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 was not pressed down.
"The properties of the Riemann zeta function..."
"The modular form of 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 condition of the Riemann zeta function, you will find that this proof essentially uses a very special symmetry of the automorphic form, that is, the weight 1/2 modulus form..."
Thinking of this, Chen Zhou looked at the documents in front of him again.
The content of the document 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 on the overall field.
Both use the self-defense form!
Chen Zhou picked up a pen, and circled the four words "self-defense form" on the previous draft paper.
Immediately, on the new draft paper, the three key words "automorphic form", "property 2 of the Riemann zeta function", and "modular form of weight 1/2" were annotated.
After doing this, Chen Zhou closed this document and opened the next one.
In fact, after sorting it out so far, the scope of the content investigated by Chen Zhou has already exceeded the scope of the subject of "Linear representation of the Artin L function of the Galois group".
In other words, the research on this topic is just a part of the content that Chen Zhou sorted out.
As the content was sorted out, Chen Zhou's strange feeling became more and more serious.
"This document? Does it have a taste?"
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 the taste is different..."
The publication time of this document is very old.
The light is the author of this document, two famous mathematicians in Japan, Goro Shimura and Toyo Taniyama.
As soon as you hear the names of these two people, you can tell that it has been a long time.
Chen Zhou was also a little surprised. Why did he find all the documents with a sense of age?
Glancing at the search page of the browser, it turned out that when Chen Zhou was searching, he only selected the search range and did not have the time to select the literature.
However, fortunately, Chen Zhou didn't miss such an excellent document because he didn't have time to select the document.
The content of this document is exactly the Taniyama-Shimura conjecture written by Chen Zhou when he sorted out the content just now.
But the content is not just the Taniyama-Shimura conjecture.
Speaking of it, the Taniyama-Shimura conjecture proposed by Shimura Goro and Taniyama Toyo can connect elliptic curves and modular forms, which is really pretty.
How about a mathematician's brain only lies in the moment when inspiration bursts out?
The content of this document, in addition to the content of the Taniyama-Shimura conjecture, also contains the content of the motivation L function.
Goro Shimura and Yutaka Taniyama made a guess from the special case of elliptic curves.
They conjectured that the motivic L functions can all be constructed from some kind of automorphic form.
In the literature, Shimura Goro's method is largely derived from algebraic geometry.
From specific calculations, he saw some exquisite special structures.
But also because of this, his method is too specific to be directly generalizable to the general case.
Chen Zhou rummaged through the downloaded documents, 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 Goro Shimura didn't generalize it to the general situation, Professor Langlands did it..."
On the draft paper, Chen Zhou began to sort out the contents of these two documents.
What Professor Langlands extended to the general situation is the famous Langlands program in modern mathematics.
Langlands' insight was that he saw a representation-theoretic core behind these structures.
He systematically introduced the infinite-dimensional representation of algebraic groups into number theory, and found a global program that can be extended to general situations.
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 reciprocal conjecture, which describes the correspondence between number theory and representation theory.
The most general guess is that Motive is equivalent to quite a few automorphic forms.
In particular it states that Galois representations should be equivalent to representations of algebraic groups.
Thus the motivic L function is equivalent to the automorphic L function.
The second part is called the functor conjecture, which describes the connection of representations between different groups...]
After writing this passage, Chen Zhou just stared at this passage, dazed.
It has to be said that the Langlands program has far-reaching significance.
It can prove the property 2 of the Riemann zeta function for the most general L function.
And derive a series of difficult conjectures, for example, Artin's conjecture.
After decades of hard work, mathematicians have made great progress in their understanding of the Langlands program.
Outstanding representative scholars, including Fields Medal winner Vladimir Drinfeld, Laurent Laforgue and Professor Wu Baozhu.
However, it is still very far from a complete program.
But it must be mentioned that the scope of the Langlands program is still expanding.
Analogous to the classic program, mathematicians have developed geometric Langlands and p-adic Langlands.
Even in physics, Professor Edward Witten proposed a similar Langlands dual.
They touch on very different fields and use very different methods.
But they both exhibit a deep level of similarity.
From different perspectives, the Langlands Program itself is enriched.
A recent, and notable, development of the Langlands program comes from the ongoing work of the genius German mathematician Peter Schulz.
Schulz used the p-adic geometric analogy function field developed by him to prove the local number field.
Thinking of this, a smile appeared on the corner of Chen Zhou's mouth.
Immediately, he took out a new draft paper and quickly wrote on it.
Chen Zhou finally knew what the strange feeling was before.
At the beginning, he just planned to sort out the research content involved in the subject of "Linear representation of the Artin L function of the Galois group".
But with the passage of time, Chen Zhou turned out to be like this. Although it was rough, it was still relatively complete. Using the Riemann ζ function and L function as clues, he sorted out modern mathematics.
And list the important issues 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, Bellingson conjecture, Artin conjecture ,Etc., etc.
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, current mathematics does not have an independent branch of mathematics in a pure sense.
Every branch of mathematics is cross-integrated.
Chen Zhou was also a little lucky.
Fortunately, I have constructed the mathematical tool of distribution deconstruction, and I am constantly improving it.
Soon, Chen Zhou stopped the pen in his hand.
On the draft paper, a schematic diagram appeared.
Chen Zhou displayed these contents in a complete way with diagrams.
There are conjectures and 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 may be enough to drain a man's life's energies.
However, it is its difficulty and profoundness that have attracted countless people.
To some extent, mathematicians and explorers are actually the same kind of people.
To be honest, from a certain point of view, whether it is Kramer's conjecture or Jebov's conjecture that Chen Zhou solved before, it is only a small part of analytic number theory.
From the perspective of modern mathematics as a whole, it is really nothing.
It can be said that it is the mathematics of smallness.
But it is also the insignificance of each step and 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 your thoughts and feelings, everything suddenly becomes clear.
A smile appeared on the corner of Chen Zhou's mouth, and he suddenly had a strange idea.
Should he thank this senior Nott?
because……
If it wasn't for Senior Sister Nott's invitation, he wouldn't have come back to sort out this part of the content.
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 that Noether said, including the Langlands program.
Originally, Nott hoped to win over Chen Zhou and conduct research together.
Efforts have been made to revive mathematics for the Knott family.
But now, it indirectly pointed out the future direction for Chen Zhou.
Of course, this is also based on Chen Zhou being able to solve Brother Guess first.
If Chen Zhou can successfully solve my brother's guess, then the direction of mathematics research will follow.
There is a high probability that it is the content he sorted out today.
Outside the window, the sky has darkened.
At this time, Chen Zhou realized that he hadn't gone to lunch because he was immersed in the world of mathematics.
This is the third time since Yang Yiyi left.
And Yang Yiyi only left for a week.
"Oh, no wonder everyone wants to marry a wife..."
Chen Zhou really missed the days when he and Yang Yiyi supervised each other, learned from each other, worked on projects together, and lived under the care of each other.
I glanced at my watch, 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 stretched his muscles a little.
When you're fully focused, you don't feel much.
With this relaxation, the exhaustion from sitting for a long time and studying suddenly surged up.
"Fortunately, I often run and exercise..." Chen Zhou said in a low voice.
However, what responded to him was the ensuing cry from the Temple of the Five Viscera.
Chen Zhou's expression froze for a moment, and he said helplessly, "Unfortunately, you won't be hungry after exercising..."
Fortunately, it's not too late at this point. Chen Zhou, who went out to look for food, had a decent supper.
Back in the dormitory again, Chen Zhou was not in a hurry to sit back at the desk.
Instead, I went to take a hot bath first to relieve the fatigue of the day.
It was only then that I once again devoted myself to the subject of looking for glue balls.
Although Chen Zhou hasn't met Ge Guess today, he has been dealing with the world of mathematics all day long.
I don't want to spend the evening time on mathematics.
Therefore, Chen Zhou started the research on the glue ball experiment again.
Now he is about to complete all 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 glue balls.
The reason is that in previous studies, physicists rarely dealt with the study of strange quantum number glue balls.
As for why so little is involved...
One reason is that strange quantum number gumballs are relatively heavy.
Another reason is that the computational analysis is relatively complex.
For example, for 0—the glue ball is still blank under the framework of the QCD summation rule.
But this, on the contrary, was the last reason why Chen Zhou didn't need to worry.
The experimental subjects he has participated in have the final perfect results.
Almost all rely on his calculations, combined with the correct direction of constant trial and error, and finally realized it.
Therefore, the theoretical research on the strange quantum number glue ball has aroused Chen Zhou's great interest.
Any goal that can be achieved by calculation.
Chen Zhou felt that those were all small goals.
(End of this chapter)
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