In the auditorium, hearing Tao Zhexuan's invitation, Xu Chuan was still a little surprised.

After all, the gap between the two is too big.

Tao Zhexuan is 41 years old this year and has won various top mathematics awards such as the Fields Medal, the Clay Research Prize, the MacArthur Prize, the Waterman Prize, and the Breakthrough Award in Mathematics.

In addition, he also has various academician honors such as Academician of the Royal Society of the Sunset, Foreign Academician of the National Academy of Sciences, Academician of the Academy of Arts and Sciences of the United States, and National Academician of Australia.

And now, he is just a college student who has proved the world-class end-of-the-world difficulty conjecture.

The difference between the two is too big.

Of course, mathematics doesn't pay much attention to these things, in the mathematics world, strength is respected, as long as you are really powerful, let alone college students, even high school students and junior high school students can get the respect of others.

As for the invitation, Xu Chuan's heartbeat was average.

Although Professor Tao Zhexuan is a Fields Medal winner, Princeton has more Fields Medal winners, and although the University of California is very good, it can be said that it is one of the three major existences second only to Puhaye in the United States, but in comparison, Princeton is undoubtedly stronger.

So he directly declined Professor Tao's invitation.

Hearing Xu Chuan's refusal, Tao Zhexuan felt sorry for a moment, but he also knew that the most suitable school for the teenager in front of him was not the University of California, Berkeley, but the one under their feet.

In mathematics alone, Princeton can beat all the other colleges and universities in the entire country.

......

After listening to Professor Schultz's lecture, Xu Chuan also returned to his hotel room.

After making a phone call to ask the hotel waiter to bring a dinner, he took out his notebook and pen from his bag and began to organize today's harvest.

Whether it was the 'p·s approach to geometry theory' explained by Professor Schultz at the lecture meeting, or the communication between the two when he met Professor Tao Zhexuan, they all brought him a lot of feelings and mathematical knowledge.

Taking advantage of the fact that this is the time when the memory is clearest in his mind, writing these things down again will help him deepen his understanding of this knowledge.

"The main conjecture of Iwasawa theory: ch(a) = ch(e/c), a is the ideal group of the number field, and is a purely algebraic object. Whereas, a rounding unit is essentially an analytical object. ”

In fact, ζ(p, s) = ζ(s) · (1. p?s)=∑p|n*1/n^s, this function is called p ζ function, it is a continuous function on zp, and its value at negative integers can be expressed by the interpolation of one of the first polynomials of zp[t]......"

“.......”

Sorting out the gains in his mind over and over again, Xu Chuan pondered whether these gains could be applied to some aspects.

It's a habit that's unique to him.

It is true that mathematics needs inspiration, but inspiration is based on knowledge.

There's a saying that 'opportunities are only reserved for those who are prepared', and if you don't prepare, you won't be able to grasp the inspiration when it comes.

"Take a suitable Garrod domain as a finite commutative group and equate algebraic objects with p-......"

When the black signature pen in his hand recorded a string of characters on the white notebook, a flash of lightning flashed in Xu Chuanhu's mind.

"Wait....... The elements of the Garohua domain can be generated from the primordial polynomial on the domain, and the domain obtained from the primordial polynomial has an additive unit of 0, a multiplication unit of 1, and a primordial polynomial of a prime polynomial. ”

"Although it is a finite domain, the Dirichlet domain can be expanded to infinity, is it possible to construct a domain value by expanding the number field, and then turn it to high latitudes, and then use the Dirichlet domain to limit the fractal dimension and the spectrum of fractal measures of the Ω?"

"The ultimate requirement of the Weyl-Berry conjecture is to prove that it is a spectral invariant of any fractal dimension and fractal measure, and if the boundary point can be given, then the spectra of the fractal dimension and fractal measure of the Ω should be determined."

"It was an idea that really inspired me at the beginning, but I didn't have enough basic knowledge to check it out, and now it seems a little flawed, but it doesn't matter, I can try it first."

Staring at the information recorded on the manuscript paper, Xu Chuan fell into deep thought.

When he had a cold last year, he was inspired to prove the Weyl-Berry conjecture, but he was unable to do it because he didn't have enough basic math.

Today, after listening to Professor Schultz's lecture on "P·S Approach - Geometric Theory" and discussing with Professor Tao Zhexuan, it seems that this opportunity has arrived.

After realizing this, Xu Chuan got up and picked up the landline at the head of the bed and called the waiter in the lobby on the first floor, asking them to send a stack of manuscript paper or printer paper.

This is a free and mandatory service at any Princeton hotel.

Because this is the mecca of mathematics, no one knows if there is a mathematician staying in the hotel, or if there is a sudden inspiration one night.

So for the sake of academics, Princeton has done everything to the best of its ability.

Soon, the waiter of the hotel sent a thick plate of manuscript paper over, along with a blessing by the way.

"Good luck, sir."

However, Xu Chuan didn't pay attention to it, he was still immersed in the idea in his mind at the moment, and after taking the manuscript paper from the little brother's hand in a godless manner, he closed the door with a bang.

The guy at the door didn't mind, working here, he met too many mathematicians, and he also saw a lot of 'weirdos'.

A customer like the one in this room doesn't even say it's weird, and ignores him, which only shows that he is immersed in thinking about a certain issue at the moment.

Although he may not look like a mathematician when he is young, he is not without young mathematicians.

For example, Professor Tao Zhexuan stayed in their hotel more than ten years ago, and that big bull also solved a mathematical conjecture in their hotel.

The latter room has been preserved as a room of special significance and is rarely open to the public.

.......

After taking the manuscript paper from the waiter's hand, Xu Chuan returned to the wooden table again.

A little beige white manuscript paper was laid out on the table, and a black ballpoint pen began to outline mathematical symbols on it.

“..... Starting from Weyl's theorem 3.2, a bounded and connected open-set Ω is constructed, and the Ω is a bounded connected region that satisfies the above conditions (≥2), and its boundary has an inner minkowski dimension δ∈(n-1,n), then there is λ→+∞, and there is:

n(λ)-?（λ）≤-，δ(λ/π2)δ/2.....pn(t+o(1))+o(δ?λ/π2)

“......”

"Let Ω(a) be a connected region, and the side length of each square is li=a(i+1)-a(i), the function a(x) is strictly monotonically increased, and limf(x→∞)=limf(x→∞)(a(x+1)-a(x))=0......"

"It is further required that the area of Ω (a) be bounded, i.e., |Ω(a)|2=∑∞/f(i=0)l2i

"Calculate the minkowski dimension 6 within the boundary and the minkowski capacity ...... on the 6-dimension"

“.......”

Based on the inspiration of the last time, Xu Chuan defined the fractal dimension of the Weyl-Berry conjecture and the spectral invariants of the fractal measure to a high-latitude boundary, and then used the Dirichlet function domain to transform the Laplace operator and the Laplace hyperbolic equation, and then expanded the domain.......

Inspiration was blowing through him again, and unlike last time, this time, he had enough basic knowledge to set up a staircase to follow his steps.

Immersed in the process of solving the proof, he is like a criminal police officer collecting evidence bit by bit at the scene of the eucalyptus, and finally bringing it together into a solid and reliable shackle to arrest the suspect hiding behind the scenes.

He is now also collecting all kinds of available and reliable mathematical knowledge bit by bit, twisting it into a reliable hemp rope, and then connecting the various mathematical theorems and computational data together to form a reliable staircase that leads to the final Weyl-Berry conjecture.

........

From the evening of the second day to the late night of the third day, for nearly thirty hours, Xu Chuan did not close his eyes.

Except for going downstairs to eat, he never stepped out of this small hotel room.

So much so that after missing the second day's party and the third day's exchange meeting and party, his senior brother Lin Feng called his mobile phone.

Hearing the vibration of the mobile phone, Xu Chuan didn't even look at it and pressed it off.

But the other party seemed to persevere, and dialed one after another, which made Xu Chuan come back to his senses from his divergent thoughts.

"Hey, Senior Brother Lin, is there anything you want to do with me?"

With a tired voice, it passed along the phone, and on the other end of the phone, Lin Feng asked with concern, "Are you okay?" Xu Chuan, did you catch a cold or what's wrong, you didn't come to today's exchange meeting and party, you missed such an important moment. ”

"I'm fine, I've been a little inspired in the past two days, thinking about problems in the room."

Xu Chuan stared at the proof data on the manuscript paper and replied.

For him, if he misses the second and third days, he misses the exchange meetings and evenings.

Although the exchange meeting is important, it is not worth mentioning at all compared to his harvest in the past two days.

This nearly thirty hours of unclosed busyness was not fruitless, using the Dicklet function domain to transform the Laplace operator and the Laplace hyperbolic equation, and then through the differential equation he finally defined a fractal framework, he succeeded in making the boundary? Ω measurable in this fractal framework.

At this point, we are only one last step away from proving the Weyl-Berry conjecture, that is, how to prove that the fractal dimension and fractal measure of Ω are spectral invariants.

As long as this problem is solved, then the Weyl-Berry conjecture becomes the Xu-Weyl-Berry theorem.

In comparison, the few sessions of the presentation and the conversations with others at the evening party are insignificant.

"Research the question? What questions to study? Forget it, you're fine, remember to rest early, and don't forget that you have a debriefing tomorrow afternoon. ”

On the other end of the phone, Lin Feng's voice was transmitted.

He hadn't seen Xu Chuan for the past two days, and he hadn't seen anyone familiar with him when he asked about it, so he was a little worried that something had happened to this little junior brother here.

After all, it's the first time I've come to the United States, and I'm not familiar with the place, plus the country doesn't ban guns, it's still a little unsafe.

As for now, since it's just a matter of studying in a hotel room, it's fine.

Although it is a pity to miss the exchange meeting and the party, it is okay for people to be fine.

.....。