Without the slightest surprise, Chen Zhou's attention was all attracted to the scanned manuscript in front of him.

The old professor is worthy of the man who has completed the transition from linear conjunctive algebra to conjugating rings.

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

This is something that has never been felt by Professor Artin.

Mathematical thinking and mathematical habits can easily have an impact on a person.

Especially people like Chen Zhou who are good at learning and changing themselves.

Chen Zhou subconsciously learned the mathematical thinking and mathematical habits of Professor Atin from these manuscript scans.

"The mutual reciprocal law found by the class domain theory that is applicable to more general cases, that is, the Atin reciprocal law......"

"Given a field of numbers on Q in which the Galois group is commutative, Artin's law of reciprocal inversion assigns an L-function to any one-dimensional representation of the Galois group, and asserts that all such L-functions are equal to some Dirichlet L-function ......"

Chen Zhou watched, learned, and thought at the same time.

The pen in his hand, as his thoughts beat, left lines of words on the scratch paper that matched the mathematics.

"The Dirichlet L-function, which is the analogy of the Riemann ζ function, is expressed by the Dirichlet feature......"

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

"Given the non-commutative Galois group and its high-dimensional representations, we can still define some naturally matched L-functions, i.e., the Artin L-functions......"

With the divergence of thinking, Chen Zhou felt more and more that something seemed to be wrong.

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

And this is not an ordinary big proposition, it is something that Chen Zhou has just sorted out and led the development of mathematics.

This thing is the Langlands Programme.

In mathematics, there are only a handful of achievements known as programmatics.

There are only three Irlangen Guidelines, Hilbert Guidelines, and Langlands Guidelines.

The Irürgen and Hilbert Programs are products of the second half of the 19th century and the beginning of the 20th century, and both of them have produced important assignments in the history of mathematics and influenced mathematics-related fields for a long time.

The Langlands Program, on the other hand, has influenced research in mathematics-related fields since its inception to this day.

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

And now he also has a tendency to study 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 the appropriate generalization of Dirichlet L-function is found, it is possible to generalize the ...... of Artin's mutual reciprocal law"

"The connection between the holopure function defined in the upper semi-complex plane and satisfying certain functional equations, i.e., the relation between the holopure self-preserving form and the Dirichlet L-function......"

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

"If the promotion is applied to the cusp of self-containment, it means ......"

The pen in Chen Zhou's hand kept rubbing on the scratch paper, leaving lines of words that matched mathematics.

With the continuous deepening of the research on this sub-topic, Chen Zhou has more and more puzzles, and there are more and more problems that need to be solved.

By 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 research of the subject.

I have to say that the manuscript of the old Professor Atin has a certain magic.

If this thing had been put aside, Chen Zhou would only have been treated as a bunch of ghost talismans.

But right now, these ghost drawings are incredibly appealing.

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

The pen in Chen Zhou's hand paused slightly.

His eyes swept over the content on the scratch paper, and he silently combed through it in his mind.

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

Whether or not it is a contradictory conjecture in the Langlands program, this subject must be done.

You can't stop there, can you?

To hesitate is to lose.

Time ticks by.

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

He sat at his desk for nearly twelve hours.

It was just after 9 a.m. when I returned to Princeton from Providence.

At this moment, the sun and the moon have changed, and it is more than 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 is still the one I bought before, and only the last bucket is left.

Just wipe it out now, and go out tomorrow to restock.

Chen Zhou has already decided, and he will adjust his study plan after eating.

Try to solve this sub-topic sent by Professor Atin first.

Then use this as a fulcrum, or opportunity, to carry out a more in-depth study of algebraic geometry.

In this way, through the study of algebraic geometry, the current distribution deconstruction method can be improved.

Finally, he solved the Goldbach conjecture that had plagued him for so long, but not much progress.

Of course, the overall learning rhythm in this is still intersecting with the rubber ball topic of physics.

Chen Zhou has always felt that this kind of interdisciplinary learning through cross-learning is conducive to the improvement of each subject.

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

"Tut-tut...... It's still delicious instant noodles!"

"Sauerkraut's is sour!"

Chen Zhouzi sucked up the instant noodles in the bucket with a snort.

Open the window to let in some air, and then start cleaning up the mess.

In the past, Chen Zhou was reluctant to add ham sausage to instant noodles, let alone braised eggs and the like.

But now he is also a millionaire.

It's not too much to add a ham sausage and a braised egg, right?

This must correspond to the identity temperament.

Chen Zhou, who was sitting at the desk again, had a hint of expectation in his eyes, and his eyes were more resolute.

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

Just like a professional person, in a field, for the cause he is familiar with, fight for a lifetime.

Because stepping into other fields always requires a certain amount of risk, and it also requires more learning.

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

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

But Chen Zhou is different, in the field of analytic number theory, he is about to stand on the ceiling.

If you want to break through, you have to step into other fields 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 math prizes, and I want to get more linguistics experience points.

Then you can't just stop at an analytic number theory.

In addition, mathematics already requires 500,000 natural science experience points from Lv7 to Lv8.

I don't know what Lv8 liter Lv9 looks like.

Chen Zhou also had to prepare for the next road in his math edifice in advance.

And now the most suitable and ideal algebraic geometry has become Chen Zhou's next stop.

"Each of the Artin's L-functions represented by finite-dimensional representations from the Galois group in a given number field is equal to an L-function represented from self-defending cusps......"

"In order to establish a one-to-one correspondence, it is necessary to consider an appropriate expansion of the Galois group, i.e., the Vey-Deligne group......"

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

In addition to the faint smell of sauerkraut, it tells that the owner here has just finished eating instant noodles.

All that's left is the sound of the tip of the pen rubbing against the scratch paper, and the sliding of the mouse wheel that only rings once in a while.

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.

Whereas, the Galois group is the group that accompanies a certain type of domain expansion.

This is also an important concept of Galois theory.

As for domain expansion, it is derived from polynomials.

The study of domain expansion and polynomials through the Galois group is known as the Galois theory.

This is knowledge that Chen Zhou is not familiar with.

Because of the content of abstract algebra, he only learned one basic.

Except for the content in abstract algebra textbooks and some literature, Chen Zhou did not have much deep understanding.

So, this is one of the reasons why Chen Zhou will be attracted to this knowledge.

The more barren it is, the more it is desired.

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

He has a deep memory of 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 on mathematical code symbols and nouns for reference at any time.

This shows that these basic contents are complicated and not easy to remember.

In fact, the reason why people with a relatively low level of mathematics read the literature of modern mathematicians feels like a book from heaven.

The biggest reason is that there are a bunch of ghostly mathematical symbols.

I don't know what these symbols mean or how they come about.

Not to mention the entire literature that is connected together.

The night was getting deeper.

Chen Zhou was still sitting straight at the desk.

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

At least until this question in front of him is resolved, Chen Zhou does not plan to sleep.

He didn't know what he knew.

"Let 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 bed at half past two in the morning, a little more than a little more.

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

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

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

The thought of not wanting to get up is getting heavier and heavier.

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

After a simple wash, Chen Zhou went out and started his morning run.

Even in Providence, the next morning when I was drunk, I didn't go for a morning run because I slept a lot.

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

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

What Chen Zhou didn't expect was.

Sister Nott, who originally thought that she would fish for three days and dry nets for two days, was also running in the morning.

And she seems to be waiting for herself intentionally.

Chen Zhou couldn't help but shake his head, it seemed that this senior sister still hadn't given up.

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

Chen Zhou was noncommittal, just smiled at her.

Chen Zhou didn't know what kind of expression the other party would have shown if he knew that he was working on the topic of "linear representation of the Artin L-function of the Galois group".

Maybe you'll be more eager to pull yourself in, right?

In other words, if this senior sister knew that Professor Deligne was also pulling herself in, I don't know what kind of expression would it be?

When Chen Zhou thought of this, he only felt that he was simply fragrant.

Whether it is a man or a woman, young or old, they all have thoughts about themselves, oops~

did not maintain the same running rhythm as Not, according to the tacit habits that he had formed with Yang Yiyi for a long time.

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

The ensuing breakfast was served by Chen Zhou at a Chinese restaurant.

Two meat buns, a bowl of tofu brain.

It's also a standard mash-up breakfast.

Back in the dormitory again, Chen Zhou rested a little before sitting at the desk again.

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

In the acquisition of the peculiar quantum number rubber ball, the moments L0 and L1 with practical operation value are obtained by using the QCD summation rule.

Chen Zhou began to calculate the mass of the peculiar quantum number rubber ball.

According to Chen Zhou's calculation results, there are two 0-rubber balls with masses of 3.81 GeV and 4.33 GeV respectively.

In addition, for the possible existence of rubber balls under these two energies, Chen Zhou also analyzed and theorized their possible generation and decay properties.

And this result also shows that it is very likely that a 0-rubber ball state can be detected on a collider that is currently in operation or planning.

It is in operation or under planning, far more than the SLAC National Accelerator Laboratory in the United States, but also the High Energy Physics Laboratory in Huaguo.

And according to Chen Zhou's understanding, the Belle experimental group of KEK in Japan has begun to prepare to find a strange quantum number rubber ball in the 0--glue ball state in the decay of the bottom quark even element.

In this regard, Chen Zhou also said that it was not possible for Japanese physicists to succeed in finding it.

But at least until it is found, there is a chance in any country.

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

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

That's what he's always done.

Maybe the sample is biased, and even this deviation can be very large.

However, with a sufficient sample size, this bias can be gradually reduced.

until it can be completely ignored eventually.

In addition, the Standard Model of particle physics has been established for more than 40 years and has undergone extensive experimental testing.

The correctness of its description of the microscopic world, at least under the TeV marker, is beyond doubt.

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

On another level, the SLAC National Accelerator Laboratory also has the first international network in North Mi.

The scientific literature database 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 regard is simply not great.

And this is where the problem set comes into play.

With the guidance of the problem set, the sample will be analyzed in the best possible way!