Xueba starts with change

Chapter 457 In-depth research (two in one 4000+)

Not surprisingly, Chen Zhou's attention was all drawn to the scanned manuscript in front of him.

Old Professor Artin is indeed a man who completed the transition from linear associative algebra to associative rings.

Looking at his manuscripts on abstract algebra research, Chen Zhou could appreciate the power of this man's mathematical thinking.

This is something that Professor Artin has never felt.

Mathematical thinking and mathematical habits can easily affect a person.

Especially someone like Chen Zhou who is good at learning and changing himself.

Subconsciously, Chen Zhou learned the mathematical thinking and mathematical habits of Professor A Ting from these scanned manuscripts.

"The law of reciprocity discovered by using the theory of class fields, which applies to more general cases, is Artin's law of reciprocity..."

"Given a number field on Q in which the Galois group is a commutative group, Artin's reciprocity law adds an L-function to any one-dimensional representation of this Galois group, and asserts that: All L-functions are equal to some Dirichlet L-functions..."

Chen Zhou watched, studied, and thought.

The pen in his hand, with the beating of his thoughts, left lines of words and mathematics on the draft paper.

"The Dirichlet L function here, which is the analogy of the Riemann zeta function, is expressed by the Dirichlet characteristic..."

"And Artin's law of reciprocity consists of the exact connection between these two L-functions..."

"Given the non-commutative Galois group and its high-dimensional representation, we can still define some natural matching L-functions, that is, Artin L-functions..."

As his thoughts diverged, Chen Zhou felt more and more that something was wrong.

According to the old Professor Artin's thinking on this unsolved problem, it will soon be extended to a big proposition.

And this is not an ordinary big proposition, it was sorted out by Chen Zhou just now, and it led the development of mathematics.

This thing is the Langlands program.

In mathematics, there are only a handful of achievements called programs.

Roughly there are only three programs: the Erlangen Program, the Hilbert Program and the Langlands Program.

The Erlangen program and the Hilbert program are the products of the second half of the 19th century to the beginning of the 20th century. They have produced important assignments in the history of mathematics and have influenced the fields of mathematics for a long time.

The Langlands program, since its birth, has been influencing research in related fields of mathematics until today.

As for why Chen Zhou felt something was wrong, it was because the Langlands program was based on Artin's L function, and after in-depth research, he extended his conjecture to the function domain and obtained more complete content.

And now, he also has a tendency to research in the direction of the Langlands program.

But now is not the time to stop.

Chen Zhou himself didn't want to stop there.

"When an appropriate generalization of Dirichlet's L-function is found, it is possible to generalize Artin's law of reciprocity..."

"A holomorphic function defined on the upper half-complex plane that satisfies some functional equations, that is, the connection between the holomorphic automorphic form and Dirichlet's L-function..."

"The self-defense cusp representation is a kind of infinite-dimensional irreducible representation of the general linear group GLn on the Q-Adair ring..."

"If the generalization is applied to self-defense cusps it means..."

The pen in Chen Zhou's hand kept rubbing against the draft paper, leaving lines of words that matched the math.

With the continuous deepening of the research on this sub-subject, Chen Zhou got more and more puzzled, and there were more and more problems to be solved.

At this time, the sky outside the window had completely darkened.

After Chen Zhou returned to the dormitory, except for the time when he entered the system space, the rest of the time was immersed in the subject research.

It has to be said that the manuscript of the old Professor Artin has a certain magical power.

If this thing is left behind, Chen Zhou will only treat it as a bunch of ghostly symbols.

But now, these ghostly symbols are extremely attractive.

"In that case, will Langlands' reciprocal conjecture be deduced sooner or later?"

The pen in Chen Zhou's hand paused slightly.

His eyes scanned the content on the draft paper, and he sorted it out silently in his heart.

After combing, the pen in Chen Zhou's hand fell on the draft paper again.

Regardless of whether it is the reciprocal conjecture in the Langlands program, this topic must be done.

You can't stop here, can you?

To hesitate is to lose.

Time ticked by.

It wasn't until after ten o'clock in the evening that Chen Zhou put down the pen in his hand and stretched himself.

He sat at the desk for nearly twelve hours.

It was just past 9 am when I returned to Princeton from Providence.

But at this moment, the sun and the moon have already changed, and it is past ten o'clock in the evening.

After boiling a pot of hot water, Chen Zhou planned to make a bucket of instant noodles to eat.

This instant noodle was bought earlier, and there is only the last bucket left.

It just happens to be wiped out now, and I will go out to replenish the stock tomorrow.

Chen Zhou has already decided to adjust his study plan after eating.

Let's try to solve the sub-project sent by Professor Arting first.

Then take this as a fulcrum, or an opportunity, to conduct a more in-depth study of algebraic geometry.

So through the study of algebraic geometry, to perfect the current distribution deconstruction method.

Finally, he will solve the Goldbach's conjecture that has troubled him for so long but has made little progress.

Of course, the overall learning rhythm here is still intersected with the rubber ball subject of physics.

Chen Zhou has always felt that this method of cross-learning between subjects is conducive to the improvement of each subject.

Moreover, it is easier to stimulate the thinking inspiration of the subject.

"Tsk tsk tsk...the instant noodles are still delicious!"

"Sauerkraut is sour!"

Chen Zhou sucked up the instant noodles in the bucket with a slur.

Open the window casually to get some air, and then start to clean up the mess.

In the past, Chen Zhou was reluctant to add ham sausage when eating instant noodles, let alone marinated eggs.

But now he is, after all, a millionaire.

It's not too much to add a ham sausage and a marinated egg, right?
This must correspond to the identity and temperament.

Chen Zhou, who was sitting in front of the desk again, had a trace of expectation in his eyes, and his eyes became more determined.

A mathematician should perhaps stick to one field and always strive for it.

Just like a professional person, in a field, he strives for a career that he is familiar with all his life.

Because setting foot in other fields always requires taking certain risks and more learning.

But even if you study hard, work hard and work hard, you may still achieve nothing in the end.

This is also the reason why many people only plan and work hard in the fields they are familiar with.

But Chen Zhou is different. In the field of analytical number theory, he is almost on the ceiling.

If you want to break through, you must set foot in other areas of mathematics.

Moreover, from the very beginning, Chen Zhou hoped to enrich his distribution deconstruction method with knowledge from other fields.

What's more, I want to win more mathematics awards and get more linguistic experience points.

Then we must not just stay in an analytic number theory.

Furthermore, Mathematics needs 7 natural science experience points from Lv8 to Lv50.

I don't know what it is like to upgrade from Lv8 to Lv9.

Chen Zhou also had to prepare in advance for his next path in the mathematics building.

Now the most suitable and ideal algebraic geometry became Chen Zhou's next stop.

"Every Artin L-function from the finite-dimensional representation of the Galois group of a given number field is equal to some L-function from the representation of an automorphic cusp..."

"If you want to establish a one-to-one correspondence, you must consider the appropriate expansion of the Galois group, that is, the Weil-Deligne group..."

As Chen Zhou immersed himself in the draft paper on the desk again, the dormitory became quiet again.

In addition to the faint smell of sauerkraut, it is telling the owner here that he just finished eating instant noodles.

All that is left is the sound of the pen nib rubbing against the draft paper, and the occasional clicking sound of the mouse wheel.

The group in the Galois group written by Chen Zhou is a relatively simple algebraic structure with only one operation.

is a basic structure that can be used to build many other algebraic systems.

A Galois group is a group that goes with some type of field expansion.

This is also an important concept of Galois theory.

As for domain expansion, it is derived from polynomials.

The study of field extensions and polynomials through Galois groups is known as Galois theory.

This is knowledge that Chen Zhou is not familiar with.

Because of the content of abstract algebra, he only learned the basics.

Except for the content in abstract algebra textbooks and some literature, Chen Zhou didn't have a deep understanding.

Therefore, this is one of the reasons why Chen Zhou is attracted by this knowledge.

The more barren, the more eager.

If you want to say that Chen Zhou is different from others, it is that his foundation is too solid.

He has a deep memory for these mathematical terms and algebraic symbols.

It will not be an obstacle to his study and research at all.

You know, even a genius like Schultz has a special cabinet for documents about mathematical code symbols and nouns for easy reference.

It can be seen that these basic contents are complicated and not easy to remember.

In fact, people with a relatively low level of mathematics feel like reading the literature of modern mathematicians.

The biggest reason is the piles of ghostly symbols like mathematical symbols.

I can't figure out what these symbols mean and how they came from.

Not to mention the entire document that is connected together.

The night was getting darker.

Chen Zhou still sat straight at the desk.

The pen in his hand is still fighting on his favorite A4 draft paper.

At least until the question in front of him is resolved, Chen Zhou doesn't intend to sleep.

He didn't know exactly when it would be.

"Assuming ρ: Gal(Q/F)→GL(m, C) is a finite-dimensional Galois representation, where F is an algebraic number field, then L(s, ρ)=p∏det(1-ρ (Frp)Np^(-s))^(-1)=(n=1→∞)∑λρ(n)/n^s..."

In the end, Chen Zhou turned off the lights and went to sleep at 02:30 in the morning, a little later.

Early the next morning, the alarm clock woke Chen Zhou up on time.

After reaching out to turn off the alarm clock, Chen Zhou got up, put on his clothes and got out of bed after only lying down for an extra minute.

It's the end of November, and the weather has officially entered the rhythm of winter.

The thought of not wanting to get out of bed was also getting heavier.

However, good living habits have always been urging Chen Zhou.

After simply washing up, Chen Zhou went out and started his morning run.

Even in Providence, it was only the next morning when I was drunk, because I slept too much and didn't go for a morning run.

During the rest of the time, Chen Zhou always maintained the habit of running in the morning.

Therefore, in the cold winter, let Chen Zhou run to keep warm.

What Chen Zhou didn't expect was that.

Sister Nott, who originally thought she would fish for three days and hang out on the nets for two days, is also jogging in the morning.

And she seemed to be intentionally waiting for herself.

Chen Zhou couldn't help shaking his head, it seems that this senior still didn't give up.

When Chen Zhou passed by Nott, Nott took the initiative to say: "After running today, I am one day closer to the one-year deadline!"

Chen Zhou was noncommittal, but just smiled at her.

Chen Zhou didn't know what kind of expression the other party would show if he knew that he was studying the subject of "Linear representation of the Artin L function of the Galois group".

Maybe you will be more eager to pull yourself into the group?

In other words, if this senior sister knew that Professor Deligne was also recruiting herself into the group, what kind of expression would she have?
Thinking of this, Chen Zhou felt that he was simply a sweet potato.

No matter men, women, young or old, everyone has their own thoughts, hey yo~
He didn't keep the same running rhythm as Nott, according to the tacit habit that he had formed with Yang Yiyi for a long time.

Chen Zhou maintained his own rhythm and completed today's morning run.

For the subsequent breakfast, Chen Zhou had it at a Chinese restaurant.

Two meat buns, a bowl of tofu nao.

It can be regarded as a standard mix and match breakfast.

Back in the dormitory again, Chen Zhou took a short rest before sitting at the desk again.

Yesterday was mathematics, so this morning, let's start with physics.

In obtaining the strange quantum number glue ball, use the moments L0 and L1 obtained by the QCD summation rule, which have practical operation value.

Chen Zhou started to calculate the mass of the strange quantum number glue ball.

According to Chen Zhou's calculation results, there are two 2-glue balls with masses of 3.81GeV and 4.33GeV respectively.

In addition, for the glueballs that may exist under these two energies, Chen Zhou also analyzed their possible production and decay properties.

And this result also shows that it is very possible to detect the 0-glue ball state on the colliders currently in operation or planned.

The ones here are in operation or planning, not only the SLAC National Accelerator Laboratory in the United States, but also the High Energy Physics Laboratory in Huaguo.

And according to Chen Zhou's knowledge, the Belle experimental group of Japan's KEK has already started to look for 0--the strange quantum number glue ball in the glue ball state in the bottom quark evenium decay.

In this regard, Chen Zhou could not say that the Japanese physicists could successfully find it.

But at least before it is found, any country has a chance.

In a sense, this also means a competition for the Nobel Prize in Physics.

After sorting out all the theoretical knowledge of the glue ball, Chen Zhou began to search for experimental literature.

This is also his usual method.

Perhaps the sample is biased, and even this bias may be large.

But in the case of enough samples, this deviation can be gradually reduced.

until it can be completely ignored.

In addition, the standard model of particle physics has been established for more than 40 years and has undergone a large number of experimental tests.

The correctness of its description of the microcosm, at least under the TeV energy scale, is beyond doubt.

Therefore, the papers and documents of these experimental studies are absolutely of reference value.

From another level, the SLAC National Accelerator Laboratory also has the first international network of Beimi.

The scientific literature database here is enough to provide a large number of experimental literature samples.

What's more, Chen Zhou also has a deviation calibration artifact.

Judging from past experience, the performance of wrong questions in this area is simply not too good.

And this is where the wrong question set plays its biggest role.

Under the guidance of the wrong question set, the sample will get the best analysis!

　Thank you book friends for the 323 starting coins rewarded by Feiyang 100 all the way!
　　
　
(End of this chapter)